Difficult
If $y = m_{1}x + c_{1}$ and $y = m_{2}x + c_{2}$ with $m_{1} \neq m_{2}$ are two common tangents of the circle $x^{2} + y^{2} = 2$ and the parabola $y^{2} = x$,then the value of $8|m_{1}m_{2}|$ is equal to
- A$3 + 4\sqrt{2}$
- B$5 - 6\sqrt{2}$
- C$3\sqrt{2} - 4$
- D$7 + 6\sqrt{2}$
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Two circles each of radius $5$ units touch each other at $(1,2)$ and $4x+3y=10$ is their common tangent. The equation of that circle among the two given circles,such that some portion of it lies in every quadrant is
Two tangents $PQ$ and $PR$ are drawn to the circle $x^2 + y^2 - 2x - 4y - 20 = 0$ from the point $P(16, 7)$. If the centre of the circle is $C$,then the area of quadrilateral $PQCR$ is ............ $sq. \text{ units}$.
DifficultIIT 1981
View SolutionGiven the circle $C$ with the equation $x^2+y^2-2x+10y-38=0$. Match the List-$I$ with the List-$II$ given below concerning $C$.
List-$I$ List-$II$ $A$. The equation of the polar of $(4, 3)$ with respect to $C$ $I$. $y+5=0$ $B$. The equation of the tangent at $(9, -5)$ on $C$ $II$. $x=1$ $C$. The equation of the normal at $(-7, -5)$ on $C$ $III$. $3x+8y=27$ $D$. The equation of the diameter passing through $(1, -5)$ and $(1, 3)$ $IV$. $x=9$
| List-$I$ | List-$II$ |
| $A$. The equation of the polar of $(4, 3)$ with respect to $C$ | $I$. $y+5=0$ |
| $B$. The equation of the tangent at $(9, -5)$ on $C$ | $II$. $x=1$ |
| $C$. The equation of the normal at $(-7, -5)$ on $C$ | $III$. $3x+8y=27$ |
| $D$. The equation of the diameter passing through $(1, -5)$ and $(1, 3)$ | $IV$. $x=9$ |
If the line $ax + y = c$ touches both the curves $x^2 + y^2 = 1$ and $y^2 = 4\sqrt{2}x$,then $|c|$ is equal to
DifficultJEE MAIN 2019
View SolutionIf $\theta$ is the angle between the curves $y^2=4x$ and $x^2+y^2=5$, then $|\tan \theta|=$
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