How to find the equation of a tangent line

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SSAT Upper Level Quantitative › How to find the equation of a tangent line

Questions 1 - 2
1

Find the equation of a tangent line at point if the function is .

Explanation

To find the slope of the tangent line, it is necessary to determine the slope of the function.

The function is already in the slope-intercept form, , and .

Substitute the slope and the given point into the slope-intercept equation.

Substitute the known slope and the y-intercept to the slope-intercept form.

2

Circle A is centered about the origin and has a radius of 5. What is the equation of the line that is tangent to Circle A at the point (–3,4)?

3_x_ – 4_y_ = –25

3_x_ + 4_y_ = 7

–3_x_ + 4_y_ = 1

3_x_ – 4_y_ = –1

Explanation

The line must be perpendicular to the radius at the point (–3,4). The slope of the radius is given by Actmath_7_113_q7

The radius has endpoints (–3,4) and the center of the circle (0,0), so its slope is –4/3.

The slope of the tangent line must be perpendicular to the slope of the radius, so the slope of the line is ¾.

The equation of the line is y – 4 = (3/4)(x – (–3))

Rearranging gives us: 3_x_ – 4_y_ = -25

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