If `C` is the center and `A ,B` are two points on the conic `4x^2+9y^2-8x-36 y+4=0` such that `/_A C B=pi/2,` then prove that `1/(C A^2)+1/(C B^2)=(13)/(36)dot`

If C is the center and A,B are two points on the conic 4x^(2)+9y^(2)-8x-36y+4=0 such that /_ACB=(pi)/(2), then prove that (1)/(CA^(2))+(1)/(CB^(2))=(13)/(36) .

If C is the center and A, B are two points on the conic 4x^2+9y^2-8x-36y+4=0 such that /_ACB=90^@ then prove that 1/(CA)^2+1/(CB)^2=13/36

Find the eccentricity of the ellipse, 4x^(2)+9y^(2)-8x-36y+4=0 .

If 4^a=36^b =9^c , then prove that (b)/(a)+(b)/( c)=1 .

In Figure, /_A C B=90dot and C D_|_A B . Prove that (C B^2)/(C A^2)=(B D)/(A D)

To remvoe the first dgree terms in the equation 4x^(2)+9y^(2)-8x+36y+4=0 , the origin in shifted to the point

The transformed equation of 4x^(2) + 9y^(2) - 8x + 36y+4=0 when the axes are translated to the point (1,-2) is

If points A and B are (1, 0) and (0, 1), respectively, and point C is on the circle x^2+y^2=1 , then the locus of the orthocentre of triangle A B C is (a) x^2+y^2=4 (b) x^2+y^2-x-y=0 (c) x^2+y^2-2x-2y+1=0 (d) x^2+y^2+2x-2y+1=0

The eccentricity of the ellipse 4x^2+9y^2+8x+36 y+4=0 is a. 5/6 b. 3/5 c. (sqrt(2))/3 d. (sqrt(5))/3

The eccentricity of the ellipse 4x^2+9y^2+8x+36 y+4=0 is 5/6 b. 3/5 c. (sqrt(2))/3 d. (sqrt(5))/3