Find an equation of the line that is tangent to the circle x² + y² = 25 at the point P ( 3, 4 ). A) $y = \frac { 3 } { 4 } x + \frac { 25 } { 4 }$ B) $y = - \frac { 4 } { 3 } x + \frac { 25 } { 3 }$ C) $y = - \frac { 3 } { 4 } x + \frac { 25 } { 4 }$ D) $y = \frac { 3 } { 4 } x - 25$ E) $y = - \frac { 3 } { 4 } x + 25$

Question

Quizplus · Accepted Answer

The slope of the radius to point P(3,4) is 4/3, so the slope of the tangent is the negative reciprocal, -3/4. Using point-slope form, the equation is $y - 4 = -\frac{3}{4}(x - 3)$, which simplifies to $y = -\frac{3}{4}x + \frac{25}{4}$.

Find an Equation of the Line That Is Tangent to the Circle