The curves `4x^2+9y^2=72` and `x^2-y^2=5a t(3,2)` touch each other (b) cut orthogonally intersect at `45^0` (d) intersect at `60^0`

The curves y=x^(2)+x+1 and 2y=x^(3)+5x touch each other at the point

If the curve ax^(2) + 3y^(2) = 1 and 2x^2 + 6y^2 = 1 cut each other orthogonally then the value of 2a :

Prove that the curves y^2=4x and x^2+y^2-6x+1=0 touch each other at the points (1,\ 2) .

Two circles x^2 + y^2 + 2x-4y=0 and x^2 + y^2 - 8y - 4 = 0 (A) touch each other externally (B) intersect each other (C) touch each other internally (D) none of these

Prove that the curves 2y^(2)=x^(3) and y^(2)=32x cut each other orthogonally at the origin

Show that the circles x^2 + y^2 - 2x-6y-12=0 and x^2 + y^2 + 6x+4y-6=0 cut each other orthogonally.

The circles x^(2)+y^(2)-12x-12y=0 and x^(2)+y^(2)+6x+6y=0 .touch each other externally touch each other internally intersect at two points none of these

Circles x^(2)+y^(2)+4x+d=0,x^(2)+y^(2)+4fy+d=0 touch each other,if

Prove that the curve 2x^(2)+3y^(2)=1 and x^(2)-y^(2)=(1)/(12) intersect orthogonally.

A point at which the ellipse 4x^(2)+9y^(2)=72 and the hyperbola x^(2)-y^(2)=5 cut orthogonally is