The line 12 x cos θ + 5 y sin θ = 60 is tangent to which of the following curves ?

Step-by-step solution

Given that 12 x   cos θ + 5 y   sin θ = 60 Divide the above equation with 60 on both sides x   cos θ 5 + y   sin θ 12 = 1 … i Let ellipse x 2 a 2 + y 2 b 2 = 1 ⇒ Equation of tangent at point ( a cos θ , b sin θ ) x a   cos θ a 2 + y b   sin θ b 2 = 1 x cos θ a + y sin θ b = 1 … i i Using equation i and i i ⇒ a = 5 b = 12 Equation of ellipse is x 2 25 + y 2 144 = 1