Answer to Question #249739 in Calculus for stan

Question #249739

At what point(s) on the circle x 2 + y 2 = 13 is its tangent line parallel to the line 3x − 2y = 6.


1
Expert's answer
2021-10-12T03:00:37-0400
"3x \u2212 2y = 6"

"y =\\dfrac{3}{2}x-3"

"slope=m=\\dfrac{3}{2}"

"x^ 2 + y^ 2 = 13"

Differentiate both sides with respect to "x" and use the Chain Rule


"2x+2yy'=0"

"x+yy'=0"

Then


"x_1+y_1y'(x_1)=0"

Substitute

"y'(x_1)=slope=m=\\dfrac{3}{2}"

"x_1+\\dfrac{3}{2}y_1=0"

"x_1=-\\dfrac{3}{2}y_1"

Point "(x_1, y_1)" lies on the circle


"x_1^2+y_1^2=13"

Then


"(-\\dfrac{3}{2}y_1)^2+y_1^2=13"

"y_1^2=4"

"y_1=\\pm2"

Point "(-3, 2)" and Point "(3, -2)."



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