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`

Which of the following line can be tangent to the parabola y^2=8x ? (a) x-y+2=0 (b) 9x-3y+2=0 (c) x+2y+8=0 (d) x+3y+12=0

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

Which of the following line can be normal to parabola y^2=12 x ? (a) x+y-9=0 (b) 2x-y-32=0 (c) 2x+y-36=0 (d) 3x-y-72=0

For which of the hyperbolas, can we have more than one pair of perpendicular tangents? (a) (x^2)/4-(y^2)/9=1 (b) (x^2)/4-(y^2)/9=-1 (c) x^2-y^2=4 (d) x y=44

Find the condition for the line y=m x to cut at right angles the conic a x^2+2h x y+b y^2=1.

Find the condition for the line y=m x to cut at right angles the conic a x^2+2h x y+b y^2=1.

The mirror image of the parabola y^2=4x in the tangent to the parabola at the point (1, 2) is (a) (x-1)^2=4(y+1) (b) (x+1)^2=4(y+1) (c) (x+1)^2=4(y-1) (d) (x-1)^2=4(y-1)

The extremities of latus rectum of a parabola are (1, 1) and (1,-1) . Then the equation of the parabola can be (a) y^2=2x-1 (b) y^2=1-2x (c) y^2=2x-3 (d) y^2=2x-4

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

Find the tangent and normal to the following curves at the given points on the curve. y = x^(4) + 2e^(x) " at " (0,2)