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Number of Tangents Drawn from a Given Point

63. Two strai...

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63. Two straight lines rotate about two fixed points (-a, 0)and (a, 0) in antic clockwise direction. If they start fromtheir position of coincidence such that one rotates at arate double of the other, then locus of curve is

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Q. Two straight lines rotate about two fixed points. If they start from their position of coincidence such that one rotates at the rate double that of the other. Prove that the locus of their point of intersection is a circle.

Q. If the lines represented by the equation

3 y^{2} - x^{2} + 2 \sqrt{3} x - 3 = 0

are rotated about the point

(\sqrt{3}, 0)

through an angle

15^{\circ}

, one in the clockwise direction and other in anti clockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is

Q. If the lines represented by the equation

3 y^{2} - x^{2} + 2 \sqrt{3} x - 3 = 0

are rotated about the point

(\sqrt{3}, 0)

through an angle

15^{0}

, one clockwise direction and other in anti-clockwise direction, then the equation of the pair of lines in the new position is

Q. A line joining two points

A (2, 0)

B (3, 1)

is rotated about

A

in anti-clockwise direction through an angle

15^{0}

C

in the new position, then the coordinates of

C

Q. The line joining two points

A (2, 0), B (3, 1)

is rotated about

A

in anti-clockwise direction through an angle of

15^{\circ}

. The equation of the line in the now position, is

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