The equation to the chord joining two points (x_1, y_1) and (x_2,… - Vidyadip

MCQ

The equation to the chord joining two points $(x_1, y_1)$ and $(x_2, y_2)$ on the rectangular hyperbola $xy = c^2$ is

✓
$\frac{x}{{{x_{1\,}}\, + \,\,{x_2}}}$+$\frac{y}{{{y_{1\,}}\, + \,\,{y_2}}}$ $ = 1$
B
$\frac{x}{{{x_{1\,}}\, - \,\,{x_2}}}$+$\frac{y}{{{y_{1\,}}\, - \,\,{y_2}}} = 1$
C
$\frac{x}{{{y_{1\,}}\, + \,\,{y_2}}}$+$\frac{y}{{{x_{1\,}}\, + \,\,{x_2}}} = 1$
D
$\frac{x}{{{y_{1\,}}\, - \,\,{y_2}}}$+$\frac{y}{{{x_{1\,}}\, - \,\,{x_2}}}= 1$

✓

Answer

Correct option: A.

$\frac{x}{{{x_{1\,}}\, + \,\,{x_2}}}$+$\frac{y}{{{y_{1\,}}\, + \,\,{y_2}}}$ $ = 1$

a
note that chord of $ xy = c^2$ whose middle point is $(h, k)$ in $\frac{x}{h}\, + \,\frac{y}{k}\, = \,2$ further, now $2h = x_1 + x_2 $ and $2k = y_1 + y_2$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The coefficient of $x^{-5}$ in the binomial expansion of ${\left( {\frac{{x + 1}}{{{x^{\frac{2}{3}}} - {x^{\frac{1}{3}}} + 1}} - \frac{{x - 1}}{{x - {x^{\frac{1}{2}}}}}} \right)^{10}}$ where $x \ne 0, 1$ , is

If $f\left( {\frac{{x - 4}}{{x + 2}}} \right) = 2x + 1,(x \in R = \left\{ {1, - 2} \right\}),$ then $\int {f(x)} \,dx$ is equal to (where $C$ is a constant of integration)

The distance between the chords of contact of tangents to the circle ; $x^2+ y^2 + 2gx+2fy+ c=0$ from the origin $\&$ the point $(g , f)$ is :

A common tangent $T$ to the curves $C_{1}: \frac{x^{2}}{4}+\frac{y^{2}}{9}=1$ and $C_{2}: \frac{x^{2}}{42}-\frac{y^{2}}{143}=1$ does not pass through the fourth quadrant. If $T$ touches $C _{1}$ at ( $\left.x _{1}, y _{1}\right)$ and $C _{2}$ at $\left( x _{2}, y _{2}\right)$, then $\left|2 x _{1}+ x _{2}\right|$ is equal to $......$

Domain of $f(x) = \log |\log x|$ is

A woman has $10$ keys out of which only one opens a lock. She tries the keys one after the another (keeping aside the failed ones) till she succeeds in opening the lock. What is the chance that it is the seventh key that works?

When $9^{th}$ term of $A.P$ is divided by its $2^{nd}$ term then quotient is $5$ and when $13^{th}$ term is divided by $6^{th}$ term then quotient is $2$ and Remainder is $5$ then find first term of $A.P.$

Let one focus of the hyperbola $H: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be at $(\sqrt{10}, 0)$ and the corresponding directrix be $x =\frac{9}{\sqrt{10}}$. If e and $l$ respectively are the eccentricity and the length of the latus rectum of H , then $9\left( e ^2+l\right)$ is equal to:

If $x = \sqrt {6 + \sqrt {6 + \sqrt {6 + ....{\rm{to}}\,\,\infty } } ,} $ then

If $y^{1 / 4}+y^{-1 / 4}=2 x$, and $\left(x^{2}-1\right) \frac{d^{2} y}{d x^{2}}+\alpha x \frac{d y}{d x}+\beta y=0$ then $|\alpha-\beta|$ is equal to ...... .