Let P (3 , 2 ) and Q (3 , 2 ) where + = 2 , be two distinct points on the hyperbola x^2 9 - y^2 4 =1 . Then the ordinate of the point of intersection of the normals at P and Q is:

Step-by-step solution

Let the coordinate at point of intersection of normals at P and Q be (h, k) Since, equation of normals to the hyperbola x^2 a^2 - y^2 b^2 =1 At point (x₁, y₁ ) is a^2 x x₁ + b^2 y y₁ =a^2+b^2 therefore equation of normal to the hyperbola x^2 3₁^2 - y^2 2^2 =1 at point P(3 , 2 ) is aligned & 3^2 x 3 + 2^2 y 2 =3^2+2^2 & 3 x +2 y =3^2+2^2 aligned Similarly, Equation of normal to the hyperbola x^2 3^2 - y^2 2^2 at point Q (3 , 2 ) is aligned & 3^2 x 3 + 2^2 y 2 =3^2+2^2 & 3 x +2 y =3^2+2^2 aligned Given + = 2 = 2 - an