The locus of the point of intersection of the lines b x t-a y t-a b and b x-a y-a b t- t being parameter isA- an ellipse with equation x 2- b 2- y 2- a 2-1B- a hyperbola with equation x2-a22-y2-b22-1C- a hyperbola with equation x 2- b 2- y 2- a 2-1D- an ellipse with equation x2-a2-y2-b2-1

The correct option is B a hyperbola with equation x^2a^2 y^2b^2 = 1Multiplying both, we get nbsp; (bx)^2 (ay)^2 = (ab)^2 ⇒x^2a^2 y^2b^2 = 1, which is t ...

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Standard XII

Mathematics

Directrix of Hyperbola

The locus of ...

Question

The locus of the point of intersection of the lines $b x t - a y t = a b$ and $b x + a y = a b t$ , $t$ being parameter is

an ellipse with equation

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

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an ellipse with equation

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

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a hyperbola with equation

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

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a hyperbola with equation

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

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Solution

The correct option is C a hyperbola with equation $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$
Multiplying both, we get
$(b x)^{2} - (a y)^{2} = (a b)^{2}$
$\Rightarrow \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ ,
which is the standard equation of hyperbola

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Similar questions

Q. The polar of any point on the ellipse

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

with respect to the hyperbola

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

The equation of normal to a hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ at a point with parameter $θ$ is

$a x c o s θ - b y c o t θ = a^{2} + b^{2}$

Q. The locus of point of intersection of pair of tangents to the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, (a > b)

if the sum of ordinates of their point of contact is half the length of minor axis, is

Q. Let

P, D

be two points on the ellipse

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

, whose eccentric angles differ by

\frac{π}{2}

. Then the locus of mid point of chord

P D

p (θ), D (θ + \frac{π}{2})

are two points on the Ellipse

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

Then the locus of point of intersection of the two tangents at P and D to the ellipse is

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Directrix of Hyperbola

Standard XII Mathematics

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The locus of the point of intersection of the lines bxt−ayt=ab and bx+ay=abt, t being parameter is

The correct option is C a hyperbola with equation x2a2−y2b2=1Multiplying both, we get (bx)2−(ay)2=(ab)2 ⇒x2a2−y2b2=1, which is the standard equation of hyperbola

The locus of the point of intersection of the lines $b x t - a y t = a b$ and $b x + a y = a b t$ , $t$ being parameter is

The correct option is C a hyperbola with equation $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$
Multiplying both, we get
$(b x)^{2} - (a y)^{2} = (a b)^{2}$
$\Rightarrow \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ ,
which is the standard equation of hyperbola