Home
Class 12
MATHS
Which of the following pair(s) of curves...

Which of the following pair(s) of curves is/are orthogonal? `y^2=4a x ; y=e^(-x/(2a))` `y^2=4a x ; x^2=4a ya t(0,0)` `x y=a^2; x^2-y^2=b^2` `y=a x ;x^2+y^2=c^2`

A

`y^(2)=4ax,y=e^(-x//2a)`

B

`y^(2)=4ax,x^(2)=4ay at (0,0)`

C

`xy=a^(2),x^(2)-y^(2)=b^(2)`

D

`y=ax,x^(2)+y^(2)=c^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise Exercise (Numerical)|12 Videos

  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise JEE Previous Year|9 Videos

  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise Exercise (Single)|48 Videos

  • 3D COORDINATION SYSTEM

    CENGAGE|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|17 Videos

Similar Questions

Explore conceptually related problems

Which one of the following curves cut the parabola at right angles? (a) x^2+y^2=a^2 (b) y=e^(-x//2a) (c) y=a x (d) x^2=4a y

The image of the pair of lines represented by a x^2+2h x y+b y^2=0 by the line mirror y=0 is a x^2-2h x y-b y^2=0 b x^2-2h x y+a y^2=0 b x^2+2h x y+a y^2=0 a x^2-2h x y+b y^2=0

Which of the following lines have the intercepts of equal lengths on the circle, x^2+y^2-2x+4y=0 (A) 3x -y= 0 (B) x+3y=0 (C) x+3y+10=0 (D) 3x-y-10=0

The locus of the moving point whose coordinates are given by (e^t+e^(-t),e^t-e^(-t)) where t is a parameter, is (a) x y=1 (b) x+y=2 (c) x^2-y^2=4 (d) x^2-y^2=2

Find centre and radius of the following circles. (i) x^(2) + ( y +2)^(2) =0 (ii) x^(2) + y^(2) + 6x -4y + 4 =0 (iii) x^(2) + y^(2) -x + 2y-3=0 (iv) 2x^(2) + 2y^(2) - 6x + 4y + 2=0

Suppose a x+b y+c=0 , where a ,ba n dc are in A P be normal to a family of circles. The equation of the circle of the family intersecting the circle x^2+y^2-4x-4y-1=0 orthogonally is (a) x^2+y^2-2x+4y-3=0 (b) x^2+y^2-2x+4y+3=0 (c) x^2+y^2+2x+4y+3=0 (d) x^2+y^2+2x-4y+3=0

Solve the following systems of equations : (i) x - 2y = 0 3x + 4y = 20 (ii) x + y = 2 2x + 2y = 4 (iii) 2x - y = 4 4x - 2y = 6

The locus of the midpoints of the chords of the circle x^2+y^2-a x-b y=0 which subtend a right angle at (a/2, b/2) is (a) a x+b y=0 (b) a x+b y=a^2=b^2 (c) x^2+y^2-a x-b y+(a^2+b^2)/8=0 (d) x^2+y^2-a x-b y-(a^2+b^2)/8=0

Which of the following is a point on the common chord of the circle x^2+y^2+2x-3y+6=0 and x^2+y^2+x-8y-31=0? (a) (1,-2) (b) (1,4) (c)(1,2) (d) 1,-4)

The area (in sq units) of the region {(x, y) : y^2 gt= 2x and x^2 + y^2 lt= 4x, x gt= 0, y gt= 0} is