Paragraph: Tangents are drawn from the point P ( 3 , 4 ) to the ellipse 9 x 2 + 4 y 2 = 1 touching the ellipse at points A and B . Question: The orthocentre of the triangle P A B is

Question

Paragraph: Tangents are drawn from the point P ( 3 , 4 ) to the ellipse 9 x 2 ​ + 4 y 2 ​ = 1 touching the ellipse at points A and B . Question: The orthocentre of the triangle P A B is

TestHub · Accepted Answer

Equation of A B is y − 0 ⇒ y ⇒ x ​ = − 5 9 ​ − 3 5 8 ​ ​ ( x − 3 ) = − 24 8 ​ ( x − 3 ) = − 3 1 ​ ( x − 3 ) + 3 y = 3 ​ Equation of the straight line perpendicular to A B through P is 3 x − y = 5 . Equation of P A is x − 3 = 0 . The equation of straight line perpendicular to P A through B ( 5 − 9 ​ , 5 8 ​ ) . is y = 5 8 ​ . Hence, the orthocentre is ( 5 11 ​ , 5 8 ​ ) .

Mathematics - Point Question with Solution | TestHub

Options:

Doubts & Discussion