If two different tangents of `y^2=4x` are the normals to `x^2=4b y ,` then `|b|>1/(2sqrt(2))` (b) `|b|<1/(2sqrt(2))` `|b|>1/(sqrt(2))` (d) `|b|<1/(sqrt(2))`

If two different tangents of y^2=4x are the normals to x^2=4b y , then (a) |b|>1/(2sqrt(2)) (b) |b| 1/(sqrt(2)) (d) |b|<1/(sqrt(2))

The slopes of the common tangents of the ellipse (x^2)/4+(y^2)/1=1 and the circle x^2+y^2=3 are +-1 (b) +-sqrt(2) (c) +-sqrt(3) (d) none of these

If the line y=mx+c is a tangent to the ellipse x^(2)+2y^(2)=4 , then the minimum possible value of c is (a) -sqrt(2) (b) sqrt(2) (c) 2 (d) 1

If the distance between the foci and the distance between the two directricies of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 are in the ratio 3:2, then b : a is (a) 1:sqrt(2) (b) sqrt(3):sqrt(2) (c) 1:2 (d) 2:1

If the distance between the foci and the distance between the two directricies of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 are in the ratio 3:2, then b : a is (a) 1:sqrt(2) (b) sqrt(3):sqrt(2) (c) 1:2 (d) 2:1

If y+b=m_1(x+a) and y+b=m_2(x+a) are two tangents to the paraabola y^2=4ax then

Normals at two points (x_1y_1)a n d(x_2, y_2) of the parabola y^2=4x meet again on the parabola, where x_1+x_2=4. Then |y_1+y_2| is equal to sqrt(2) (b) 2sqrt(2) (c) 4sqrt(2) (d) none of these

Tangents are drawn to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a > b), and the circle x^2+y^2=a^2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then the greatest acute angle between these tangents is given by (A) tan^(-1)((a-b)/(2sqrt(a b))) (B) tan^(-1)((a+b)/(2sqrt(a b))) (C) tan^(-1)((2a b)/(sqrt(a-b))) (D) tan^(-1)((2a b)/(sqrt(a+b)))

Find the equations of the tangent and the normal to the curve (x^2)/(a^2)-(y^2)/(b^2)=1 at (sqrt(2)a ,\ b) at indicated points.

The line x-y+2=0 touches the parabola y^2 = 8x at the point (A) (2, -4) (B) (1, 2sqrt(2)) (C) (4, -4 sqrt(2) (D) (2, 4)