Question

${a}^{2} {y}^{2} = {x}^{2} ( {a}^{2} - {x}^{2} )$

Find the tangent of this curve

urgent 55 points​

Answer 1

Answer:

${a}^{2} {y}^{2} = {x}^{2} ( {a}^{2} - {x}^{2} )$

Tangent at origin of this curve are

${a}^{2} {y}^{2} = {a}^{2} {x}^{2}$

${y}^{2} - {x}^{2}$

y=-x and x

Two tangents ,real and distinct

Answer 2

Explanation:

The line y = mx + c meets the ellipse x2/a2 + y2/b2 = 1 in two real, coincident or imaginary points according as c2 < = or > a2m2 + b2.

Hence, y = mx + c is tangent to the ellipse x2/a2 + y2/b2 = 1 if c2 = a2m2 + b2.

The equation of the chord to the ellipse joining two points with eccentric angles α and β is given by

x/a cos ((α + β)/2) + y/b sin ((α + β)/2) = cos ((α - β)/2)