If `y= A cos 4x + Bsin 4x` , `A` and `B` are constants then show that `y_2 + 16y = 0 `

If y = A cos 4 x + B sin 4 x, A and B are constants then Show that y_2 + 16y =0

If y = A cos 4x + b sin 4x, (d^(2)y)/(dx^(2)) +ky=0 , find k:

The line 4x+2y = c is a tangent to the parabola y^(2) = 16x then c is :

A-=(-4,0),B-=(4,0)dotMa n dN are the variable points of the y-axis such that M lies below Na n dM N=4 . Lines A Ma n dB N intersect at Pdot The locus of P is a. 2x y-16-x^2=0 b. 2x y+16-x^2=0 c. 2x y+16+x^2=0 d. 2x y-16+x^2=0

If a cos (x + y) = b cos (x - y), show that (a + b)tan x = (a - b) cot y.

If y= 3 cos (log x)+4 sin(log x) , show that x^(2)y_(2)+xy_(1)+y=0 .

If x + y = 0 is the angle bisector of the angle containing the point (1,0), for the line 3x + 4y + b = 0; 4x+3y + b =0, 4x + 3y- b = 0 then

Show that the equation of the circle passing through (1, 1) and the points of intersection of the circles x^2+y^2+13 x-3 y=0 and 2x^2+2y^2+4x-7y-25=0 is 4x^2+4y^2+30 x-13 y-25=0.

If the lines x - y - 1 = 0, 4x + 3y = k and 2x – 3y +1 = 0 are concurrent, then k is

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 .