Dasmani M.
asked • 06/22/20find the equation of the tangent to x^2 +y^2 =5 which has a gradient is -2.
This is a circle, of course.
Implicit differentiation gives dy/dx=-x/y=-2, i.e. y=x/2
Substitution: x2 + (x2/4) = 4 => x=±2 and that means y=±1 so there will be 2 tangents.
One of these is -2=(y-1)/(x-1) and you can "massage" this into any form you need.
I will leave it to you to get the equation of the other tangent in a similar way.
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Joe V.
5.0 (1,332)
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5.0 (1,666)
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Tom K.
You could also solve without calculus by noting that the tangent will be perpendicular to the circle's radius. Of course, orthogonal means that the slope is the negative reciprocal.06/23/20