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Equation of Normal at Given Point

Assertion :St...

Question

Assertion :Statement-l : The combined equation of both the axes of the hyperbola $x y = c^{2}$ is $x^{2} - y^{2} = 0$ Reason: Statement - 2 : Combined equation of axes of hyperbola is the combined equation of angle bisectors of the asymptotes of the hyperbola.

Both statements are true and Statement 2 is the correct explanation of Statement 1.

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Both statements are true and Statement 2 is not the correct explanation of Statement 1.

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Statement 1 is true and Statement 2 is false.

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Statement 1 is false and Statement 2 is true.

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Solution

The correct option is A Both statements are true and Statement 2 is the correct explanation of Statement 1.
We know that equation of axis for hyperbola $x y = k$ is given by
$x = y$ and $x = - y$ . Combined equation of both the axis can be writtten as $x^{2} - y^{2} = 0$

And Statement 2 gives a proper definition of axis.

Suggest Corrections

Similar questions

1 :

x y + y z + z x = 1

x, y, z \in R^{+}

\frac{x}{1 + x^{2}} + \frac{y}{1 + y^{2}} + \frac{z}{1 + z^{2}} = \frac{2}{\sqrt{(1 + x^{2}) (1 + y^{2}) (1 + z^{2})}}

2 :

A B C

sin 2 A + sin 2 B + sin 2 C = 4 sin A sin B sin C

Choose the correct option.

Statement $1 : (p \land \sim q) \land (\sim p \land q)$ is a fallacy.

Statement $2 : (p \Rightarrow q) \Leftrightarrow (\sim q \Rightarrow\sim p)$ is a tautology.

4^{\circ} C

(p \lor q) \land \sim p

\sim p \land q

Statement 1:

(\sqrt{- 3 + 4 x - x^{2}} + 4)^{2} + (x - 5)^{2}

1 \leq x \leq 3)

36.

Statement 2:

(5, - 4)

(x - 2)^{2} + y^{2} = 1

6

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