Question

Find the equation of the tangent at the point (h, h) to the curve x² + y² = a²
1. hx + hy =a²
2. hx - hy = a²
3. x + hy = a
4. hx - y = - a

Answer 1

Correct Answer - Option 1 : hx + hy =a²

Concept:

Equation of the tangent at the point (x1, y1) to the curve x2 + y2 = a² is given by:

xx1 + yy1 = a2

 

Calculation:

The given equation is,

x2 + y2 = a²

We know that for any given circle, the equation of the tangent passing through the point (x₁, y₁) is

xx₁ + yy₁ = a²

So, the given point is (h,h)

Hence, the equation of the tangent is,

hx + hy =a2