The equation of the parabola whose vertex and focus lie on the axis of `x` at distances `a` and `a_1` from the origin, respectively, is (a) `y^2-4(a_1-a)x` (b) `y^2-4(a_1-a)(x-a)` (c) `y^2-4(a-a_1)(x-a)` (d) none of these

Find the equation of the parabola whose vertex is (4, -2) and focus is (1, -2).

If same force is acting on two masses m_1 and m_2 and the accelerations of two bodies are a_1 and a_2 respectively, then

The eccentric angle of a point on the ellipse (x^2)/4+(y^2)/3=1 at a distance of 5/4 units from the focus on the positive x-axis is cos^(-1)(3/4) (b) pi-cos^(-1)(3/4) pi+cos^(-1)(3/4) (d) none of these

Prove that the equation of the parabola whose focus is (0, 0) and tangent at the vertex is x-y+1 = 0 is x^2 + y^2 + 2xy - 4x + 4y - 4=0 .

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 axis of a parabola is along the line y=x and the distance of its vertex and focus from the origin are sqrt(2) and 2sqrt(2) , respectively. If vertex and focus both lie in the first quadrant, then the equation of the parabola is (x+y)^2=(x-y-2) (x-y)^2=(x+y-2) (x-y)^2=4(x+y-2) (x-y)^2=8(x+y-2)

Let y=x+1 is axis of parabola, y+x-4=0 is tangent of same parabola at its vertex and y=2x+3 is one of its tangents. Then find the focus of the parabola.

The coordinates of a point on the parabola y^2=8x whose distance from the circle x^2+(y+6)^2=1 is minimum is (2,4) (b) (2,-4) (18 ,-12) (d) (8,8)

A B C is a variable triangle such that A is (1,2) and B and C lie on line y=x+lambda (where lambda is a variable). Then the locus of the orthocentre of triangle A B C is (a) (x-1)^2+y^2=4 (b) x+y=3 (c) 2x-y=0 (d) none of these

The locus of a point on the variable parabola y^2=4a x , whose distance from the focus is always equal to k , is equal to ( a is parameter) (a) 4x^2+y^2-4k x=0 (b) x^2+y^2-4k x=0 (c) 2x^2+4y^2-9k x=0 (d) 4x^2-y^2+4k x=0