Given:

Vertices (±7, 0) and e = \( \dfrac{4}{3}\)

Here, the vertices are on the x- axis

The equation of the hyperbola is of the form

\( \dfrac{x^2}{a^2}\) +\( \dfrac{y^2}{b^2}\) = 1,

Since, the vertices are (± 7, 0), so, a = 7

It is given that e = \( \dfrac{4}{3}\)

\( \dfrac{c}{a}\) = \( \dfrac{4}{3}\)

3c = 4a

Substitute the value of a, we get

3c = 4(7)

c = \( \dfrac{28}{3}\)

It is known that, a^{2} + b^{2} = c^{2}

7^{2} + b^{2} = (\( \dfrac{28}{3}\))^{2}

b^{2} = \( \dfrac{784}{9}\) – 49

= \( \dfrac{(784 – 441)}{9}\)

= \( \dfrac{343}{9}\)

The equation of the hyperbola is

\( \dfrac{x^2}{49}- \dfrac{9y^2}{343}=1\)

Answered by Abhisek | 11 months agoAn equilateral triangle is inscribed in the parabola y^{2} = 4ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.

Find the area of the triangle formed by the lines joining the vertex of the parabola x^{2} = 12y to the ends of its latus rectum.

A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.

An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.