Let the tangent drawn to the parabola y 2 = 24 x at the point α , β is perpendicular to the line 2 x + 2 y = 5 . Then the normal to the hyperbola x 2 α 2 - y 2 β 2 = 1 at the point α + 4 , β + 4 does NOT pass through the point:

Step-by-step solution

Given, the tangent drawn to the parabola y 2 = 24 x at the point α , β is perpendicular to the line 2 x + 2 y = 5 . So, tangent at α , β has slope 1 And α , β lies on y 2 = 24 x so β 2 = 24 α Equation of tangent will be y β = 12 x + α so its slope will be 12 β = 1 , so β = 12 ⇒ α = 6 , β = 12 ∴     α + 4 , β + 4 = 10 , 16 Now finding normal at 10 , 16 to x 2 36 - y 2 144 = 1 , First finding slope of the tangent 2 x