The points on the circle are (6, 8) and (-6, -8)
The equation that represents the circle is given as:
Circle equation: x^2 + y^2 = 100
The slope is given as:
Slope: m = 3/4
Start by differentiating the circle equation.
This is done as follows:
So, we have:
2x x' + 2y y' = 0
Divide through the equation by 2
x x' + y y' = 0
Subtract x x' from both sides of the equation
y y' = -x x'
This gives
y'/x' = -x/y
The expression represents the slope.
So, we have:
x/y = 3/4
Make x the subject
x = 3y/4
Substitute x = 3y/4 in x^2 + y^2 = 100
(3y/4)^2 + y^2 = 100
Evaluate the exponent
9y^2/16 + y^2 = 100
Multiply through by 16
9y^2 + 16y^2 = 1600
This gives
25y^2 = 1600
Divide by 25
y^2 = 64
Take the square root
y = ±8
Substitute y = ±8 in x = 3y/4
x = 3 * ±8/4
This gives
x = ±6
Hence, the points on the circle are (6, 8) and (-6, -8)
Read more about circle equations at:
https://brainly.com/question/1559324
#SPJ1
