The line $2x - y + 1 = 0$ is tangent to the circle at the point $(2, 5)$ and the centre of the circles lies on $x-2y=4$. The radius of the circle is
The line $2x - y + 1 = 0$ is tangent to the circle at the point $(2, 5)$ and the centre of the circles lies on $x-2y=4$. The radius of the circle is
- A
$3 \sqrt{5}$
- B
$5 \sqrt{3}$
- C
$2 \sqrt{5}$
- D
$5 \sqrt{2}$
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Circles $x^2 + y^2 + 4x + d = 0, x^2 + y^2 + 4fy + d = 0$ touch each other, if
Circles $x^2 + y^2 + 4x + d = 0, x^2 + y^2 + 4fy + d = 0$ touch each other, if
Consider the following statements :
Assertion $(A)$ : The circle ${x^2} + {y^2} = 1$ has exactly two tangents parallel to the $x$ - axis
Reason $(R)$ : $\frac{{dy}}{{dx}} = 0$ on the circle exactly at the point $(0, \pm 1)$.
Of these statements
Consider the following statements :
Assertion $(A)$ : The circle ${x^2} + {y^2} = 1$ has exactly two tangents parallel to the $x$ - axis
Reason $(R)$ : $\frac{{dy}}{{dx}} = 0$ on the circle exactly at the point $(0, \pm 1)$.
Of these statements
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Tangents drawn from origin to the circle ${x^2} + {y^2} - 2ax - 2by + {b^2} = 0$ are perpendicular to each other, if
Tangents are drawn from the point $(4, 3)$ to the circle ${x^2} + {y^2} = 9$. The area of the triangle formed by them and the line joining their points of contact is
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If the tangent at $\left( {1,7} \right)$ to the curve ${x^2} = y - 6$ touches the circle ${x^2} + {y^2} + 16x + 12y + c = 0$ then the value of $c$ is:
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