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write an equation of the line that is tangent to the circle at the given point.x^2+y^2=24

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x^2+y^2=24; (-2*square root of 2, -4)

asked Feb 27, 2014 in ALGEBRA 2 by rockstar Apprentice

2 Answers

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A line tangent to a circle and radius to the point of tangency are perpendicular.

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answered Feb 27, 2014 by ashokavf Scholar
edited Feb 27, 2014 by ashokavf
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The circle is x2 + y2 = 24 and the point is (- 2√2, - 4).

Differentiate with respect to x.

2x + 2y y ' = 0

x + y y ' = 0

y y ' = - x

⇒ y ' = - x/y.

When, x = - 2√2 and y = - 4,  y ' = - ( - 2√2 )/- 4 = - 1/√2.

y ' = - 1/√2.

This is the slope (m ) of the tangent line to the circle at (- 2√2, - 4).

Slope - intercept form line equation is y = mx + b, where m is slope and b is y - intercept.

Slope(m) = - 1/√2.

Now the tangent line equation is y = (- 1/√2)x  + b.

Find the y - intercept by substituting the the point in the tangent line equation say (x, y) = (- 2√2, - 4).

- 4 = (- 1/√2)(- 2√2) + b

b = - 4 - 2

⇒ b = - 6.

The tangent line equation  is y = (- 1/√2)x - 6.

answered Jun 18, 2014 by lilly Expert

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