Question

The slope of the tangent at the point (h, h) of the circle x2 + y2 = a²
1. 1
2. -1
3. 0
4. 2

Answer 1

Correct Answer - Option 2 : -1

Concept:

For any straight line y= mx + c, m = slope or gradient and c = intercept

The equation of the tangent at the point (x1,y1) on the circle 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 at the point (x1,y1) on the circle is

xx1 + yy1 = a2

So, the given point is (h, h)

Hence, the equation of the tangent is,

hx + hy =a²

⇒y = -x + \(\rm a^2 \over h\)

Comparing the equation with y = mx + c the slope will be -1.