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=90^@ then prove that 1/(CA)^2+1/(CB)^2=13/36

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

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

If the lines joining the points of intersection of the curve 4x^(2)+9y+18xy=1 and the line y=2x+c the origin are equally inclined to the y-axis,the c is: -1 (b) (1)/(3)( c) (2)/(3)(d)-(1)/(2)

if a,b,c are in G.P. and a^(x)=b^(y)=c^(z) prove that (1)/(x)+(1)/(z)=(2)/(y)

Which of the following is/are true? There are infinite positive integral values of a for which (13 x-1)^2+(13 y-2)^2=((5x+12 y-1)^2)/a represents an ellipse. The minimum distance of a point (1, 2) from the ellipse 4x^2+9y^2+8x-36 y+4=0 is 1 If from a point P(0,alpha) two normals other than the axes are drawn to the ellipse (x^2)/(25)+(y^2)/(16)=1 then |alpha|<9/4dot If the length of the latus rectum of an ellipse is one-third of its major axis, then its eccentricity is equal to 1sqrt(3)

Let (x,y) be a variable point on the curve 4x^(2)+9y^(2)-8x-36y+15=0 then min(x^(2)-2x+y^(2)-4y+5)+max(x^(2)-2x+y^(2)-4y+5)

If e_(1) is the eccentricity of the conic 9x^(2)+4y^(2)=36 and e_(2) is the eccentricity of the conic 9x^(2)-4y^(2)=36 then e12-e22=2 b.e22-e12=2c.2 3

If area of an equilateral triangle inscribed in the circle x^(2)+y^(2)+10x+12y+c=0 is 27sqrt(3), then the value of c is (a) 25(b)-25 (c) 36(d)-36