Question

The line / is tangent to the circle x^2+y^2=50 at the point A.

Answer 1

Answer:

175 sq units

Step-by-step explanation:

The equation of the circle is

$x^2+y^2 = 50$

Tangent at point (1,7) will have slope equal to its derivative value

Differentiate to get

$2x+2yy1 = 0\\y1 = \frac{-x}{y} =\frac{-1}{7}$

Using point slope formula

$y-7 = \frac{-1}{7} (x-1)\\y = \frac{-1}{7}x+ \frac{50}{7}$

this line cuts x axis at (50,0) P

The triangle OAP has vertices equal to (0,0) (1,7) and (50,0)

The triangle has base as OP = 50 units

Height = distance of A from x axis = 7

Area = $\frac{1}{2} bh\\= 175$ sq units