Question

Here is a circle, centre O, and the tangent to the circle at the point (-3, 4) on the circle. У P (-3, 4) X -5 O Oา Find an equation of the tangent at the point P. Give your answer in the form y = ax + b where a and b are both fractions with denominator 4. ​

Answer 1

Answer:

$y=\frac{3}{4}x+\frac{25}{4}$

Step-by-step explanation:

when a line is tangent to a circle, it is perpendicular to the line from the center of the circle to the intersection of the line and the circle. so first we are going to find the slope of the line in the circle.

to find the slope use the formula $\frac{y_2-y_1}{x_2-x_1}$

$\frac{4-0}{-3-0}=\frac{4}{-3}=-\frac{4}{3}$ so the slope is -4/3

the slope of the line perpendicular to this is the opposite reciprocal: 3/4 so now we have y= 3/4 x +b, to find b plug in the point (-3,4) to get 4=-9/4 +b, b=25/4 the equation is y=3/4 x +25/4