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If the line 3x+4y=sqrt7 touches the elli...

If the line `3x+4y=sqrt7` touches the ellipse `3x^(2)+4y^(2)=1`, then find the point of contact.

Text Solution

Verified by Experts

Equation of given tangent is
`3x+4y=sqrt(7)`
Let the line touch the given ellipse at point `P(x_(1),y_(1))" "(1)`
Thus, eqution of tangent toe ellipse at point P is
`3x x_(1)+4yy_(1)=1" "(2)`
Equation (1) an (2) represent the ame stright line.
`:. (3x_(1))/(3)=(4y_(1))/(4)=(1)/(sqrt7)`
`:. P(x_(1),y_(1))-=((1)/(sqrt7),(1)/(sqrt(7)))`
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