Consider two curves $C_1 : y^2 = 2x$ and $C_2 : x^2 + y^2 - 3x + 2 = 0$. Then,
- A$C_1$ and $C_2$ touch each other only at one point
- B$C_1$ and $C_2$ touch each other exactly at two points
- C$C_1$ and $C_2$ intersect (but do not touch) at exactly two points
- D$C_1$ and $C_2$ neither intersect nor touch each other
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Similar Questions
Let the circles $C_1 : |z| = r$ and $C_2 : |z - 3 - 4i| = 5, z \in \mathbb{C}$,be such that $C_2$ lies within $C_1$. If $z_1$ moves on $C_1, z_2$ moves on $C_2$ and $\min |z_1 - z_2| = 2$,then $\max |z_1 - z_2|$ is equal to:
DifficultJEE MAIN 2026
View SolutionIf the tangent at the point $\left(4 \cos 2 \theta, \frac{16}{\sqrt{11}} \sin 2 \theta\right)$ on the ellipse $16 x^2+11 y^2=256$ touches the circle $x^2+y^2-2 x=15$,then $\theta=$
$A(x_1, y_1)$ is the internal centre of similitude and $B(x_2, y_2)$ is the external centre of similitude of two circles $C_1$ and $C_2$ whose centres are $P(\alpha, \beta)$ and $Q(\gamma, \delta)$ respectively. If $PA=3, AB=5, QB=2$,then the ratio of the radii of the two circles is:
DifficultTS EAMCET 2022
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 image of the point $(-4, 5)$ in the line $x + 2y = 2$ lies on the circle $(x + 4)^2 + (y - 3)^2 = r^2$,then $r$ is equal to:
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