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

Number of intersecting points of the conic 4x^(2) + 9y^(2) = 1 and 4x^(2) + y^(2) = 4 is _

The coodinates of the centre of the hyperbola 4x ^(2) -9y^(2) +8x+36y=68 are-

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))

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))

Find the equation to the ausiliary circle of the ellipse 4x^(2) +9y^(2) -24x - 36 y + 36 = 0 .

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

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

A tangent at a point on the circle x^2+y^2=a^2 intersects a concentric circle C at two points Pa n dQ . The tangents to the circle X at Pa n dQ meet at a point on the circle x^2+y^2=b^2dot Then the equation of the circle is (a) x^2+y^2=a b (b) x^2+y^2=(a-b)^2 (c) x^2+y^2=(a+b)^2 (d) x^2+y^2=a^2+b^2

If y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+c)=0 , then