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`

Let A (0,2),B and C be points on parabola y^(2)+x +4 such that /_CBA (pi)/(2) . Then the range of ordinate of C is

In A B C ,a , ca n dA are given and b_1,b_2 are two values of the third side b such that b_2=2b_1dot Then prove that sinA=sqrt((9a^2-c^2)/(8c^2))

If points Aa n dB 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

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

If the length of a focal chord of the parabola y^2=4a x at a distance b from the vertex is c , then prove that b^2c=4a^3dot

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)

Identify the type of conic section for each of the following equations: 4x^(2)-9y^(2)=36

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 two lines represented by x^4+x^3y+c x^2y^2-x y^3+y^4=0 bisect the angle between the other two, then the value of c is (a) 0 (b) -1 (c) 1 (d) -6