SSAT Upper Level Math : How to find the equation of a tangent line

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

Example Question #1 : Coordinate Plane

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)?

Possible Answers:

3x – 4y = –25

3x + 4y = 7

3x – 4y = –1

–3x + 4y = 1

Correct answer:

3x – 4y = –25


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: 3x – 4y = -25



Example Question #1 : How To Find The Equation Of A Tangent Line

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

Possible Answers:

Correct answer:


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.

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