To find: The equation of the tangent line
Answer to Problem 53AYU
The equation of the tangent line is
Explanation of Solution
Given:
Calculation:
Since the containing the center and the tangent line are perpendicular, the product of their slopes will be -1.Let
The standard form of an equation of a circle with its center at the origin and the radius
Since the given circle
The product of
The slope
The tangent also has the point
So, the point-slope form of the equation of the tangent can be written using
Multiply the numerator and denominator of right-hand side of the equation by
Multiply both side of the equation by 4 to clear the fraction
Remove the parentheses using the distributive property
Subtract
Conclusion:
Hence,the equation of the tangent line is
Chapter 1 Solutions
Precalculus
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