Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas 5y2 – 9x2 = 36

Asked by Sakshi | 1 year ago |  48

1 Answer

Solution :-


The equation is 5y2 – 9x2 = 36

Let us divide the whole equation by 36, we get

\( \dfrac{5y^2}{36} – \dfrac{9x^2}{36} =\dfrac{ 36}{36}\)

\(\dfrac{ y^2}{(\dfrac{36}{5})} – \dfrac{x^2}{4} = 1\)

On comparing this equation with the standard equation of hyperbola \(\dfrac{ y^2}{a^2} – \dfrac{x^2}{b^2} = 1\)

We get a =\( \dfrac{6}{\sqrt{5}}\) and b = 2,

It is known that, a2 + b2 = c2


c2 = \(\dfrac{ 36}{5} + 4\)

c2 = \( \dfrac{ 56}{5}\)

c = \( \sqrt{\dfrac{56}{5}}\)

= \( \dfrac{2\sqrt{14}}{\sqrt{5}}\)


The coordinates of the foci are (0,\( \dfrac{2\sqrt{14}}{\sqrt{5}}\)) and (0, –\( \dfrac{2\sqrt{14}}{\sqrt{5}}\)).

The coordinates of the vertices are (0,\( \dfrac{6}{\sqrt{5}}\)) and (0,\( \dfrac{-6}{\sqrt{5}}\))

Eccentricity, e =\(\dfrac{c}{a}\) = (\( \dfrac{2\sqrt{14}}{\sqrt{5}}\))\( \dfrac{6}{\sqrt{5}}\) = \( \dfrac{14}{\sqrt{3}}\)

Length of latus rectum = \( \dfrac{ 2b^2}{a} \)

\(\dfrac{(2 × 2^2)}{\dfrac{6}{\sqrt{5}}}\)

\( \dfrac{(2 × 4)}{\dfrac{6}{\sqrt{5}}}\)


Answered by Aaryan | 1 year ago

Related Questions

An equilateral triangle is inscribed in the parabola y2 = 4ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

Class 11 Maths Conic Sections View Answer

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.

Class 11 Maths Conic Sections View Answer

Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum.

Class 11 Maths Conic Sections View Answer

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.

Class 11 Maths Conic Sections View Answer

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.

Class 11 Maths Conic Sections View Answer