On the ellipse `4x^2+9y^2=1,` the points at which the tangents are parallel to the line `8x=9y` are (a) `(2/5,1/5)` (b) `(-2/5,1/5)` `(-2/5,-1/5)` (d) `(2/5,-1/5)`

A point on the ellipse x^2+3y^2=37 where the normal is parallel to the line 6x-5y=2 is (5,-2) (b) (5, 2) (c) (-5,2) (d) (-5,-2)

Find the equation of tangent of the curve y^(2) = 4x+5 which is parallel to the line 2x-y=5 .

The coordinates of the orthocentre of the triangle formed by the lines 2x^2 - 2y^2 + 3xy + 3x+y+1=0 and 3x+2y+1=0 are (A) (4/5, 3/5) (B) (- 3/5, - 1/5) (C) (1/5, - 4/5) (D) (2/5, 1/5)

Equation of the tangents to the ellipse x^2/9 + y^2/16 = 1 which are parallel to the line x+y+1=0 are (A) x+y+5=0 (B) x+y-5=0 (C) x+y+6=0 (D) x+y-6=0

Find the equation of the tangents of the hyperbola 4x ^(2) - 9y ^(2) = 36, which are parallel to the line 5x - 3y =2.

If the tangent drawn to parabola y=x^2-5x+5 at a point is parallel to 2y=4x+lamda . Then the tangent passes through the point. (A) (3/4, 5/2) (B) (-1/8, 7) (C) (1,3) (D) (1/8,-7)

The angle between the normals of ellipse 4x^2 + y^2 = 5 , at the intersection of 2x+y=3 and the ellipse is (A) tan^(-1) (3/5) (B) tan^(-1) (3/4) (C) tan^(-1) (4/3) (D) tan^(-1) (4/5)

Show that the line joining the points (4,5) and (1,2) is parallel to the line joining the points (9,-2) and (12,1) .

The point on the circle (x-3)^2 + (y-4)^2 = 4 which is at least distance from the circle x^2 + y^2 = 1 is : (A) (3/5, 4/5) (B) (9/5, 12/5) (C) (9, 12) (D) none of these

Find the angle between the two lines : (x+1)/(2)=(y-2)/(5)=(z+3)/(4)and(x-1)/(5)=(y+2)/(2)=(z-1)/(-5)