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_1-a)(x-a)` (d) ` n o n e `

Prove that the equation of the parabola whose vertex and focus are on the X-axis at a distance a and a'from the origin respectively is y^2=4(a'-a)(x-a)

The capacitance of the capacitors of plate areas A_1 and A_2(A_1 lt A_2) at a distance d is

The capacitance of capacitor of plate areas A_1 and A_2 ( A_1 ltA_2 at a distance d is

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 (a) (x+y)^2=(x-y-2) (b) (x-y)^2=(x+y-2) (c) (x-y)^2=4(x+y-2) (d) (x-y)^2=8(x+y-2)

If the equation of the locus of a point equidistant from the points (a_1,b_1) and (a_2,b_2) is (a_1-a_2)x+(b_2+b_2)y+c=0 , then the value of C is

If the equation of the locus of a point equidistant from the points (a_1, b_1) and (a_2, b_2) is (a_1-a_2)x+(b_1-b_2)y+c=0 , then find the value of c .

Let f(x)=(sqrt2^x -2)/(sqrt2^x +2) then if the graphs of y=f(x) and y=f(4x) are symmetrical about the points (a_1,0) and (a_2,0) respectively then a_2/a_1=

If A_1 is the area of the parabola y^2=4 ax lying between vertex and the latusrectum and A_2 is the area between the latusrectum and the double ordinate x=2 a , then A_1/A_2 is equal to

If one of the roots of the equation ax^2 + bx + c = 0 be reciprocal of one of the a_1 x^2 + b_1 x + c_1 = 0 , then prove that (a a_1-c c_1)^2 =(bc_1-ab_1) (b_1c-a_1 b) .

The ratio in which the line segment joining points A(a_1,\ b_1) and B(a_2,\ b_2) is divided by y-axis is (a) -a_1: a_2 (b) a_1: a_2 (c) b_1: b_2 (d) -b_1: b_2