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`

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

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

Prove that in a A B C ,sin^2A+sin^2B+sin^2C<=9/4dot

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

If the points A (x,y), B (1,4) and C (-2,5) are collinear, then shown that x + 3y = 13.

If tanthetaa n dsectheta are the roots of a x^2+b x+c=0, then prove that a^4=b^2(b^2 - 4ac)dot

If area of an equilateral triangle inscribed in the circle x^2+y^2+10x+12y+c=0 is 27sqrt3 , then the value of c is (a) 25 (b) -25 (c) 36 (d) -36

If tantheta and sectheta are the roots of a x^2+b x+c=0, then prove that a^4=b^2(b^2-4ac)dot

C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangent at any point P on this hyperbola meet the straight lines b x-a y=0 and b x+a y=0 at points Qa n dR , respectively. Then prove that C QdotC R=a^2+b^2dot

Let P be any moving point on the circle x^2+y^2-2x=1. A B be the chord of contact of this point w.r.t. the circle x^2+y^2-2x=0 . The locus of the circumcenter of triangle C A B(C being the center of the circle) is a. 2x^2+2y^2-4x+1=0 b. x^2+y^2-4x+2=0 c. x^2+y^2-4x+1=0 d. 2x^2+2y^2-4x+3=0