The radius of the circle r = $\sqrt{3}\sin \left(\mathrm{\theta }\right) + \cos \left(\mathrm{\theta }\right)$ is

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The equation of the circle whose diameter is the common chord of the circles x² + y² + 2x + 3y + 2 = 0 and x² + y² + 2x - 3y - 4 = 0 is

• x² + y² + 2x + 2y + 2 = 0

• x² + y² + 2x + 2y - 1 = 0

• x² + y² + 2x + 2y + 1 = 0

• x² + y² + 2x + 2y + 3 = 0

If x - y + 1 = 0 meets the circlex² + y² + y - 1 = 0 at A and B, then the equation of the circle with AB as diameter is

• 2(x² + y²) + 3x - y + 1 = 0

• 2 (x² + y²) + 3x - y + 2 = 0

• 2(x² + y²) + 3x - y + 3 = 0

• x² + y² + 3x - y + 1 = 0

If y = 3x is a tangent to a circle with centre (1, 1), then the other tangent drawn through (0, 0) to the circle is

• 3y = x

• y = - 3x

• y = 2x

• y = - 2x

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The line among the following which touches the parabola y = 4ax, is

• x + my + am² = 0

• x - my + am² = 0

• x + my - am² = 0

• y + mx + am² = 0

Which of the following equations gives a circle ?

• $\mathrm{r} = 2\sin \left(\mathrm{\theta }\right)$

• ${\mathrm{r}}^2\cos \left(2\mathrm{\theta }\right) = 1$

• $\mathrm{r}\left(4\cos \left(\mathrm{\theta }\right) + 5\sin \left(\mathrm{\theta }\right)\right) = 3$

• $5 = \mathrm{r}\left(1 + \sqrt{2}\cos \left(\mathrm{\theta }\right)\right)$

Let O be the origin and A be a point on the curve y = 4x. Then the locus of the mid point of OA is :

• x² = 4y

• x² = 2y

• y² = 16x

• y² = 2x

The number of common tangents to the two circles x² + y - 8x + 2y = 0 and x² + y² - 2x - 16y + 25 = 0 is :

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Observe the following statements :

I. The circle x² + y² - 6x - 4y - 7 = 0 touches y-axis.

II. The circle x² + y² + 6x + 4y - 7 = 0 touches

x-axis. Which of the following is a correct statement ?

• Both I and II are true

• Neither I nor II is true

• I is true, II is false

• I is false, II is true

The length of the tangent drawn to the circle x² + y² - 2x + 4y - 11 = 0

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