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JEE • MATHEMATICS • TANGENTS & NORMALS

Tangents & normals practice · Mixed difficulty

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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 271-281 of 281 questions

271 Easy

271 of 281

Application +4 | -1

m

is the slope of the tangent to the curve

e^y=1+x^2

, then

View answer and explanation

Correct option: D

|m| \leq 1

Option D (

|m| \leq 1

) is correct because the slope of the tangent,

|m|

, is always less than or equal to 1, as derived using AM-GM inequality.

272 Easy

272 of 281

Analyzing +4 | -1

The two curves

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

and

3 x^2 y-y^3=2

View answer and explanation

Correct option: A

Cut at right angles

Option A (Cut at right angles) is correct because the product of the slopes of the tangents to the two curves at their point of intersection is -1.

273 Easy

273 of 281

Analyzing +4 | -1

At which point the line

\frac{x}{a}+\frac{y}{b}=1

, touches the curve

y=b e^{-x i a}

View answer and explanation

Correct option: C

(0, b)

Option C ((0, b)) is correct because it is the point where the line and the curve have the same slope, indicating tangency.

274 Medium

274 of 281

Application +4 | -1

The slope of the tangent to the curve

x = 3{t^2} + 1,\;y = {t^3} - 1

, at

x = 1

View answer and explanation

Correct option: A

Option A (0) is correct because the slope of the tangent is found by differentiating the parametric equations and evaluating at the given x value.

275 Medium

275 of 281

Analyzing +4 | -1

If the curves

\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\,and\,\frac{{{x^2}}}{{{l^2}}} - \frac{{{y^2}}}{{{m^2}}} = 1

cut each other orthogonally, then

View answer and explanation

Correct option: C

{a^2} - {b^2} = {l^2} + {m^2}

Option C (

{a^2} - {b^2} = {l^2} + {m^2}

) is correct because it is derived from the condition for orthogonal intersection of the two given curves.

276 Medium

276 of 281

Analyzing +4 | -1

The two curves

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

and

3{x^2}y - {y^3} - 2 = 0

View answer and explanation

Correct option: A

Cut at right angel

Option A (Cut at right angel) is correct because the product of the slopes of the tangents to the curves at the point of intersection is -1.

277 Medium

277 of 281

Application +4 | -1

The tangent to the curve

y = 2{x^2} - x + 1

is parallel to the line

y = 3x + 9

at the point

View answer and explanation

Correct option: D

\left( {1,2} \right)

Option D ((1,2)) is correct because at this point, the derivative of the curve equals the slope of the line, indicating a parallel tangent.

278 Medium

278 of 281

Application +4 | -1

The point

P

of the curve

{y^2} = 2{x^3}

such that the tangent at P is perpendicular to the line

4x - 3y + 2 = 0

is given by

View answer and explanation

Correct option: D

\left( {1/8,\; - 1/16} \right)

Option D ((1/8, -1/16)) is correct because the tangent at this point is perpendicular to the given line.

279 Easy

279 of 281

Application +4 | -1

The point on the curve

y=(x-1)(x-2)

at which the tangent makes an angle of

135^{\circ}

with the positive direction of

x

-axis has coordinates

View answer and explanation

Correct option: A

(1,0)

Option A ((1,0)) is correct because at this point, the derivative of the curve equals -1, which corresponds to a tangent angle of 135 degrees with the x-axis.

280 Easy

280 of 281

Analyzing +4 | -1

If the parabolas

{y^2} = 4x

and

{x^2} = 32y

intersect at

\left( {16,8} \right)

at an angle

\theta ,

then

\theta

is equal to

View answer and explanation

Correct option: A

{\tan ^{ - 1}}\left( {3/5} \right)

Option A (

{\tan ^{ - 1}}\left( {3/5} \right)

) is correct because it is the angle between the tangents to the parabolas at the point of intersection, calculated using the slopes of the tangents.

281 Medium

281 of 281

Application +4 | -1

The abscissa of the point on the curve

a{y^2} = {x^3}

, the normal at which cuts off equal intercepts from the coordinate axes is

View answer and explanation

Correct option: B

4\;a/9

Option B (

4\\;a/9

) is correct because it represents the x-coordinate where the normal to the curve cuts off equal intercepts, derived by equating the x and y intercepts of the normal's equation.

Revision notes and key takeaways

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

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