The graph of x 2 a 2-y 2 b 2-1 is symmetric about

We know that if the equation nbsp;y=f(x) contains even powers of x such as nbsp;x2,x4,x6 nbsp;etc., then its graph will be symmetric about y axis. Similar ...

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Byju's Answer

Standard XII

Mathematics

Graph of Functions x^(2n)

The graph of ...

Question

The graph of $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ is symmetric about

x-axis

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y-axis

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origin

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both x-axis and y-axis

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Solution

The correct option is D both x-axis and y-axis
We know that if the equation $y = f (x)$ contains even powers of x such as $x^{2}$ , $x^{4}, x^{6} e t c$ ., then its graph will be symmetric about y-axis.
Similarly, if the equation
x = f(y), contains the even powers of y, then its graph will be symmetric about x-axis.
Here, the given equation contains even power term of both x and y. Hence, its graph is symmetric about both x-axis and y-axis.

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Similar questions

Q. Find the condition for the following set of curves to intersect orthogonally:

(i)

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 and x y = c^{2}

(ii)

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 and \frac{x^{2}}{A^{2}} - \frac{y^{2}}{B^{2}} = 1

Q. An ellipse has a focus at

(a e, 0)

and directrix along

x = \frac{a}{e}

. If

b^{2} = a^{2} (1 - e^{2})

, then the equation of ellipse is

If the eccentricities of the hyperbolas $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 a n d \frac{y^{2}}{b^{2}} - \frac{x^{2}}{a^{2}} = 1$ be e and $e_{1}$ , then $\frac{1}{e^{2}} + \frac{1}{e_{1}^{2}} =$

Q. Show that the curves

\frac{x^{2}}{a^{2} + λ_{1}} + \frac{y^{2}}{b^{2} + λ_{1}} = 1 and \frac{x^{2}}{a^{2} + λ_{2}} + \frac{y^{2}}{b^{2} + λ_{2}} = 1

intersect at right angles.

Q. Let a, b, c be positive real numbers. The following system of equations in x, y and z

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} - \frac{z^{2}}{c^{2}} = 1, \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1, - \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1 has

(a) no solution
(b) unique solution
(c) infinitely many solutions
(d) finitely many solutions

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The graph of x2a2−y2b2=1 is symmetric about

The graph of $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ is symmetric about