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JEE • MATHEMATICS • TRANSFORMATION OF AXES

Transformation of axes practice · Medium

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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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1 Medium

1 of 10

Application +4 | -1

The pedal points of a perpendicular drawn from origin on the line

3 x+4 y-5=0

, is

View answer and explanation

Correct option: B

\left(\frac{3}{5}, \frac{4}{5}\right)

Option B ((3/5), (4/5)) is correct because it represents the coordinates of the foot of the perpendicular from the origin to the line.

2 Medium

2 of 10

Application +4 | -1

If the origin is shifted to the point

(a b /(a-b), 0)

without rotation, then the equation

(a-b)\left(x^2+y^2\right)-2 a b x-0

becomes -

View answer and explanation

Correct option: D

(a-b)^2\left(x^2+y^2\right)-a^2 b^2

Option D (

(a-b)^2(x^2+y^2)-a^2 b^2

) is correct because shifting the origin and substituting into the equation leads to this result after simplification.

3 Medium

3 of 10

Application +4 | -1

The point

(4,1)

undergoes the following two successive transformation

(i) Reflection about the line

y=x

(ii) Translation through a distance 2 units along the positive

x

-axis

Then the final coordinates of the point are

View answer and explanation

Correct option: B

(3,4)

Option B ((3,4)) is correct because after reflection about y=x, (4,1) becomes (1,4), and then translation by 2 units along the x-axis results in (3,4).

4 Medium

4 of 10

Understanding +4 | -1

If by rotating the coordinate axes without translating the origin, the expression

a_1 x^2+2 h_1 x y+b_1 y^2

becomes

a_2 X^2+2 h_2 X Y+b_2 Y^2

, then

View answer and explanation

Correct option: B

a_1+b_1=a_2+b_2

Option B is correct because

a_1 + b_1

is invariant under rotation of axes.

5 Medium

5 of 10

Application +4 | -1

If the coordinates of two points

A

and

B

are

(3,4)

and

(5,-2)

respectively. Then, the coordinates of any point

P

, if

P A=P B

and area of

\triangle P A B=10

, are

View answer and explanation

Correct option: B

(7,2),(1,0)

Option B ((7,2),(1,0)) is correct because these points satisfy both the condition PA=PB and the area condition of the triangle PAB.

6 Medium

6 of 10

Analyzing +4 | -1

If by rotating the coordinate axes without translating the origin, the expression

a_1 x^2+2 h_1 x y+b_1 y^2

becomes

a_2 X^2+2 h_2 X Y+b_2 Y^2

, then

View answer and explanation

Correct option: A

\left(a_1-b_1\right)^2+4 h_1^2=\left(a_2-b_2\right)^2+4 h_2^2

Option A

\left((a_1 - b_1)^2 + 4h_1^2 = (a_2 - b_2)^2 + 4h_2^2\right)

is correct because it represents an invariant under rotation of coordinate axes.

7 Medium

7 of 10

Application +4 | -1

A B C

is a variable triangle with the fixed vertex

C(1,2)

and

A, B

having the coordinates

(\cos t, \sin t),(\sin t,-\cos t)

respectively, where

t

is a parameter. The locus of centroid of the

\triangle A B C

View answer and explanation

Correct option: B

3\left(x^2+y^2\right)-2 x-4 y+1=0

Option B (

3(x^2+y^2)-2x-4y+1=0

) is correct because it represents the locus of the centroid of the triangle ABC, derived by eliminating the parameter t.

8 Medium

8 of 10

Application +4 | -1

The transformed equation of

{x^2} + 6xy + 8{y^2} = 10

when the axes are rotated through an angle

\frac{\pi }{4}

View answer and explanation

Correct option: C

15{x^2} + 14xy + 3{y^2} = 20

Option C (

15{x^2} + 14xy + 3{y^2} = 20

) is correct because after rotating the axes by

\frac{\pi}{4}

, the transformed equation is

15{x^2} + 14xy + 3{y^2} = 20

9 Medium

9 of 10

Analyzing +4 | -1

x = X\cos \theta - Y\sin \theta ,y = X\sin \theta + Y\cos \theta

and

{x^2} + 4xy + {y^2} = A{X^2} + B{Y^2},0 \le \theta \le \frac{\pi }{2},

then

View answer and explanation

Correct option: B

\theta = \frac{\pi }{4}

Option B (

\theta = \frac{\pi }{4}

) is correct because substituting the given transformations into the equation and comparing coefficients leads to the condition that

\theta = \frac{\pi}{4}

10 Medium

10 of 10

Application +4 | -1

If the equation

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

is transformed to the equation

2{X^2} + {Y^2} - 8X - 8Y + 18 = 0

by shifting the origin at a point

P

without rotating the coordinates axes, then the coordinates of

P

are

View answer and explanation

Correct option: D

\left( { - 1, - 2} \right)

Option D ((-1,-2)) is correct because it represents the shift in origin that transforms the first equation into the second.

Revision notes and key takeaways

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

Key Takeaways

✓ This set contains 10 single-correct-answer MCQs on TRANSFORMATION OF AXES.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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