Tangents are drawn from a point on the circle x^2+y^2=11 to the parabola x^2/36 - y^2/25=1 then tangents are at angle?

Dear student,

The equation for a straight line in the point-slope form is

Substituting for m gives

Clearing fractions, we have

but

Adding equations (3.5) and (3.6) yields

Dividing by y₁ gives

which is an equation of a straight line in the slope-intercept form. This is the equation of the tangent line to the parabola

at the point (x₁,y₁).

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All the best.

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