The point x1- y1 lies outside- on or inside the hyperbola x2a2 -y2b2 - 1 depending upon

The correct option is B x_1^2a^2 y_1^2b^2 1 0 .If the point ( x_1, y_1 ) lies outside, on or inside #160;the hyperbola x^2/a^2 y^2/b ...

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Standard XII

Mathematics

Four Common Forms of Parabola Equation

The point x...

Question

The point $(x_{1}, y_{1})$ lies outside, on or inside the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ depending upon

\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1 >, =

< 0

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\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} + 1 >, =

< 0

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\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1 <, =

> 0

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\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} + 1 <, =

> 0

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Solution

The correct option is B $\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1 <, =$ or $> 0$ .
If the point $(x_{1}, y_{1})$ lies outside, on or inside the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ then $\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1 <, =$ or $> 0$ .

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Similar questions

If $P (x_{1}, y_{1})$ is such that $\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} > 1$ .

Then the point P situates outside the standard hyperbola $\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} >= 1$ .

Q. Assertion :The point

(7, - 3)

relative to hyperbola

9 x^{2} - 4 y^{2} = 36

lies inside it. Reason: If the point

(x_{1}, y_{1})

lies outside the hyperbola

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

then

\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1 > 0

Q. Statement-l : The point

(7, - 3)

lies inside the hyperbola

9 x^{2} - 4 y^{2} = 36

where as the point

(2, 7)

lies outside this.
Statement-2: The point

(x_{1}, y_{1})

lies outside, on or inside the hyperbola

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

according as

\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1 < o r = o r > 0

If for the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, S_{1} = \frac{x_{1}^{2}}{a^{2}} + \frac{y_{1}^{2}}{b^{2}} - 1$ , for point $(x_{1}, y_{1})$ , Which of the following is true

(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2} = a^{2}

;

(x_{2} - x_{3})^{2} + (y_{2} - y_{3})^{2} = b^{2}

;

(x_{3} - x_{1})^{2} + (y_{3} - y_{1})^{2} = c^{2}

;
then find

4 {∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣}^{2} =

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The point (x1,y1) lies outside, on or inside the hyperbola x2a2−y2b2=1 depending upon

The correct option is B x21a2−y21b2−1<,= or >0.If the point (x1,y1) lies outside, on or inside the hyperbola x2a2−y2b2=1 then x21a2−y21b2−1<,= or >0.

The point $(x_{1}, y_{1})$ lies outside, on or inside the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ depending upon

The correct option is B $\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1 <, =$ or $> 0$ .
If the point $(x_{1}, y_{1})$ lies outside, on or inside the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ then $\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1 <, =$ or $> 0$ .