If the normal to the rectangular hyperbola x 2 - y 2 = 1 at the point P π 4 meets the curve again at Q θ , then sec 2 θ + tan θ =

Step-by-step solution

Given, Equation of hyperbola x 2 - y 2 = 1 Now parametric point is given by a sec θ , b tan θ ≡ 2 , 1 as given θ = 45 °   &   a = b = 1 Now finding slope of tangent at the given point by differentiating the curve we get, 2 x - 2 y d y d x = 0 ⇒ d y d x 2 , 1 = 2 1 So, slope of normal will be - 2 , Now equation of normal will be y = - x 2 + 2 Since normal is intersecting the curve again so, x 2 - - x 2 + 2 2 = 1 ⇒ x 2 + 4 2 x - 10 = 0 ⇒ x = 2   or