Equations of tangents

[sudhir]

Find the equations of tangents to ellipse 9x squre + 16y squre = 144 , which pass through the pt. ( 2 , 3 ).

Kindly find the solution.

Sudhir

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[stapel]

Kindly find the solution.
Sudhir
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Thank you.

Eliz.

 

[Unco]

Find the equations of tangents to ellipse 9x squre + 16y squre = 144 , which pass through the pt. ( 2 , 3 ).

One way:

Let a point on the ellipse where the tangent passes through (2, 3) be (p, q).

Differentiate the ellipse's equation implicitly to obtain an expression for the slope of the curve at (p, q).

Set this equal to the slope of a straight line passing though (p, q) and (2, 3).

Pull out the ellipse's equation (=144) from that and you'll be away.

Show your progress if need be.

(A sketch is always the starting point; you'll see one of the solutions from this, too.)

 

[Denis]

Find the equations of tangents to ellipse 9x squre + 16y squre = 144

Your equation properly typed: 9x^2 + 16y^2 = 144