Vertex of the parabola $9{x^2} - 6x + 36y + 9 = 0$ is

$\left( { - 1/3, - 1/2} \right)$

The vertex of the parabola ${x^2} + 2y = 8x - 7$ is

$\left( {\frac{9}{2},0} \right)$

$\left( {2,\frac{9}{2}} \right)$

$\left( {4,\frac{7}{2}} \right)$

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JEE • MATHEMATICS • PARABOLA

Parabola practice · Easy

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 211-240 of 356 questions

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211 Easy

211 of 356

Analyzing +4 | -1

a \neq 0

and the line

2 b x+3 c y+4 d=0

passes through the points of intersection of the parabolas

y^2=4 a x

and

x^2=4 a y

, then

View answer and explanation

Correct option: D

d^2+(2 b+3 c)^2=0

Option B (

(a / 2,0)

) is incorrect. The correct answer is C (

(a, 0)

) because the locus of the midpoints is another parabola whose focus is at (a,0).

212 Easy

212 of 356

Application +4 | -1

Equation of a normal to the parabola

y^2=32 x

passing through its focus is

View answer and explanation

Correct option: B

y=0

Option B (

y=0

) is correct because it represents a normal to the parabola that passes through its focus, derived from the normal equation and the focus coordinates.

213 Easy

213 of 356

Application +4 | -1

The point on the curve

{y^2} = ax

the tangent at which makes an angle of

{45^0}

with

x

-axis will be given by

View answer and explanation

Correct option: C

\left( {a/4,a/2} \right)

Option C (

\left( {a/4,a/2} \right)

) is correct because it represents the point on the parabola where the tangent makes a 45-degree angle with the x-axis, calculated using the tangent's slope.

214 Easy

214 of 356

Application +4 | -1

The focal distance of a point on the parabola

y^2=16 x

, whose ordinate is twice the abscissa, is

View answer and explanation

Correct option: B

Option B (8) is correct because substituting the ordinate-abscissa relationship into the parabola equation and calculating the focal distance yields 8.

215 Easy

215 of 356

Application +4 | -1

Vertex of the parabola

9{x^2} - 6x + 36y + 9 = 0

View answer and explanation

Correct option: A

\left( {1/3, - 2/9} \right)

Option A ( (1/3, -2/9) ) is correct because it represents the vertex obtained after rewriting the given parabola equation in standard form.

216 Easy

216 of 356

Application +4 | -1

The axis of the parabola

9 y^2-16 x-12 y-57=0

View answer and explanation

Correct option: A

3 y=2

Option A (

3 y=2

) is correct because it represents the axis of symmetry of the given parabola after completing the square.

217 Easy

217 of 356

Application +4 | -1

The slopes of tangents drawn from a point

(4,10)

to the parabola

y^2=9 x

, are

View answer and explanation

Correct option: B

1 / 4,9 / 4

Option B (

1/4, 9/4

) is correct because these are the slopes of the tangents found by substituting the point (4, 10) into the tangent equation of the parabola.

218 Easy

218 of 356

Understanding +4 | -1

Eccentricity of the parabola

x^2-4 x-4 y+4=0

View answer and explanation

Correct option: B

e=1

Option B (

e=1

) is correct because the eccentricity of a parabola is always equal to 1.

219 Easy

219 of 356

Analyzing +4 | -1

y = mx + 4

is a tangent to both the parabolas,

{y^2} = 4x

and

\mathrm{ }{x^2} = 2by,

then

b

is equal to

View answer and explanation

Correct option: B

-128

Option B (-128) is correct because by finding the tangent to the first parabola and then using the condition of tangency for the second parabola, we can solve for the value of b.

220 Easy

220 of 356

Application +4 | -1

The value of

c

, for which the line

y = 2x + c

, is tangent to the parabola

{y^2} = 4a\left( {x + a} \right)

, is

View answer and explanation

Correct option: D

\frac{{5a}}{2}

Option D (

\frac{{5a}}{2}

) is correct because it is found by substituting the line equation into the parabola equation and setting the discriminant to zero, then solving for

c

221 Easy

221 of 356

Application +4 | -1

Equation of the directrix of parabola

2{x^2} = 14y

is equal to

View answer and explanation

Correct option: A

y = - \frac{7}{4}

Option A (

y = - \frac{{7}}{{4}}

) is correct because the equation of the directrix of the parabola is

y = -a

, where

a = \frac{7}{4}

222 Easy

222 of 356

Analyzing +4 | -1

The graph represented by the equations

x = {\sin ^2}t,y = 2\cos t,

View answer and explanation

Correct option: B

A parabola

Option B (A parabola) is correct because eliminating the parameter t results in an equation of the form

{y^2} + 4x = 4

, which represents a parabola.

223 Easy

223 of 356

Application +4 | -1

In the parabola

{y^2} = 4ax

, the length of the chord passing through the vertex inclined to the axis at

\frac{\pi }{4}

View answer and explanation

Correct option: A

4a\sqrt 2

Option A (

4a\sqrt 2

) is correct because it represents the length of the chord passing through the vertex of the parabola at an angle of

\frac{\pi}{4}

224 Easy

224 of 356

Analyzing +4 | -1

Let

l_1

and

l_2

be the two lines which are normal to

y^2=4 x

and tangent to

y^2=-12 y

respectively (where

l_1

and

l_2

are not the

{x}

-axis ). Then, the product of the slopes of

l_1

and

l_2

View answer and explanation

Correct option: B

Option B (2) is correct because solving for the slopes of the normal and tangent lines leads to the product of the slopes being 2.

225 Easy

225 of 356

Application +4 | -1

If the focus and vertex of a parabola are the points

\left( {0,2} \right)

and

\left( {0,4} \right)

respectively, then its equation is

View answer and explanation

Correct option: C

{x^2} + 8y = 32

Option C (

{x^2} + 8y = 32

) is correct because it represents a parabola with the given focus and vertex, derived by using the definition of a parabola and its directrix.

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226 Easy

226 of 356

Application +4 | -1

The vertex of the parabola

{x^2} + 2y = 8x - 7

View answer and explanation

Correct option: B

\left( {4,\frac{9}{2}} \right)

Option B (

(4,\frac{9}{2})

) is correct because it represents the vertex of the parabola after rewriting the given equation in the standard form.

227 Easy

227 of 356

Application +4 | -1

The parametric coordinates of any point on the parabola whose focus is

(0,1)

and the directrix is

x+2=0

, are

View answer and explanation

Correct option: D

\left(t^2-1,2 t+1\right)

Option D (

t^2-1,2 t+1

) is correct because these parametric coordinates satisfy the equation of the parabola with focus (0,1) and directrix x+2=0.

228 Easy

228 of 356

Application +4 | -1

The line

y=m x+1

is a tangent to the parabola

y^2=4 x

, if

m=

View answer and explanation

Correct option: A

Option A (1) is correct because substituting the line equation into the parabola equation and applying the tangency condition (c = a/m) yields m = 1.

229 Easy

229 of 356

Application +4 | -1

The equation of the chord of

y^2=8 x

which is bisected at

(2,-3)

, is

View answer and explanation

Correct option: A

4 x+3 y+1=0

Option A (

4 x+3 y+1=0

) is correct because the equation of the chord bisected at a given point is found using the formula T = S', where T and S' are calculated based on the given parabola and the point of bisection.

230 Easy

230 of 356

Application +4 | -1

The line

2 x+y+\lambda=0

is a normal to the parabola

y^2=-8 x

, if

\lambda=

View answer and explanation

Correct option: C

Option C (24) is correct because substituting the equation of the normal into the parabola equation and solving for lambda gives 24.

231 Easy

231 of 356

Application +4 | -1

The equation

x^2-2 x y+y^2+3 x+2=0

represents

View answer and explanation

Correct option: A

A parabola

Option A (A parabola) is correct because the discriminant

h^2 - ab = 0

indicates that the equation represents a parabola.

232 Easy

232 of 356

Application +4 | -1

The equation of the tangent to the parabola

y^2=4 a x

at point

\left(a / t^2, 2 a / t\right)

View answer and explanation

Correct option: A

t y=x t^2+a

Option B (

ty=x+at^2

) is correct because it is the equation of the tangent to the parabola

y^2=4ax

at the point

(\frac{a}{t^2}, \frac{2a}{t})

233 Easy

233 of 356

Analyzing +4 | -1

Two perpendicular tangents

P A

and

P B

are drawn to

y^2=4 a x

, minimum length of

A B

is equal to

View answer and explanation

Correct option: C

4 a

Option C (

4a

) is correct because the minimum length of AB is the length of the latus rectum, which is

4a

234 Easy

234 of 356

Application +4 | -1

The line

y=2 x+c

is tangent to the parabola

y^2=4 x

, then what is the value of

c

View answer and explanation

Correct option: B

1 / 2

Option B (

1/2

) is correct because it satisfies the tangency condition for a line to be tangent to a parabola.

235 Easy

235 of 356

Application +4 | -1

If the parabola

y^2=4 a x

passes through

(3,2)

, then the length of its latusrectum, is

View answer and explanation

Correct option: B

4 / 3

Option B (4 / 3) is correct because substituting (3,2) into the equation allows us to solve for 'a', and then calculate the latus rectum 4a.

236 Easy

236 of 356

Application +4 | -1

2x + y + k = 0

is a normal to the parabola

{y^2} = - 8x,

then the values of

k

View answer and explanation

Correct option: D

The correct answer is D (24) because it represents the value of k for which the given line is normal to the parabola.

237 Easy

237 of 356

Application +4 | -1

From the point

\left( { - 1, - 6} \right)

two tangents are drawn to the parabola

{y^2} = 4x

. Then, the angle between the two tangents is

View answer and explanation

Correct option: D

{90^0}

The correct answer is D (

{90^0}

) because the product of the slopes of the two tangents is -1, indicating they are perpendicular.

238 Easy

238 of 356

Application +4 | -1

The latus rectum of the parabola

y^2=5 x+4 y+1

View answer and explanation

Correct option: C

Option C (5) is correct because after completing the square, the equation is in the form

(y-k)^2 = 4p(x-h)

, and the latus rectum is

4p

239 Easy

239 of 356

Application +4 | -1

The vertex of the parabola

9 x^2-6 x+36 y+9=0

View answer and explanation

Correct option: A

(1 / 3,-2 / 9)

Option A (

(1 / 3,-2 / 9)

) is correct because completing the square and rewriting the equation in vertex form reveals the vertex coordinates.

240 Easy

240 of 356

Application +4 | -1

The length of the latusrectum of the parabola

2\left\{(x-a)^2+(y-a)^2\right\}=(x+y)^2

, is

View answer and explanation

Correct option: B

2 \sqrt{2} a

Option B (

2 \sqrt{2} a

) is correct because it is calculated using the distance between the focus and directrix of the parabola.

Revision notes and key takeaways

Review PARABOLA in your textbook or class notes, then use this set to check your understanding.

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