Pair of Tangent - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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18 Questions around this concept.
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MEDIUMThe tangents to having inclinations
and
intersect at
. If
, then the locus of
is
If the two tangents are drawn on hyperbola in such a way that the product of their gradients is
, then they intersect on the curve:
The angles between a pair of tangents drawn from a point P to the circle $\mathrm{x^2+y^2+4 x-6 y+9 \cos ^2 \alpha+13 \sin ^2 \alpha=0 \text { is } 2 \alpha \text {. }}$. The equation of the locus of the point P, is
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The angle between the two tangents from the origin to the circle $\mathrm{(x-7)^{2}+(y+1)^{2}=25}$ equals
Concepts Covered - 1
Pair of Tangent
Pair of Tangent
The combined equation of the pair of tangents drawn from $P\left(x_1, y_1\right)$ to the circle $S: x^2+y^2=a^2$ is
$
\left(x^2+y^2-a^2\right)\left(x_1^2+y_1^2-a^2\right)=\left(x x_1+y y_1-a^2\right)^2 \quad \text { or } \quad S S_1=T^2
$
Where,
$
\begin{aligned}
& S \equiv x^2+y^2-a^2 \\
& S_1 \equiv x_1^2+y_1^2-a^2 \\
& T \equiv x x_1+y y_1-a^2
\end{aligned}
$
The combined equation of a pair of tangents drawn from $\mathrm{P}\left(\mathrm{x}_1, \mathrm{y}_1\right)$ to a circle $x^2+y^2+2 g x+2 f y+c=0$ is
$
S S_1=T^2
$
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