The inverse point of (1, 2) with respect to the circlex2 + y

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 Multiple Choice QuestionsMultiple Choice Questions

311.

The sides of the rectangle of greatest area that can be inscribed in the ellipse x2 + 4y2 = 64 are :

  • 62, 42

  • 82, 42

  • 82, 82

  • 162, 42


312.

The polar equation of the circle with centre 2, π2 are radius 3 units is:

  • r2 + 4rcosθ = 5

  • r2 + 4rsinθ = 5

  • r2 - 4rsinθ = 5

  • r2 - 4rcosθ = 5


313.

The equation of the circle of radius 3 that lies in the fourth quadrant and touching the lines x = 0 and y = 0 is

  • x2 + y2 - 6x + 6y + 9 = 0

  • x2 + y2 - 6x - 6y + 9 = 0

  • x2 + y2 + 6x - 6y + 9 = 0

  • x2 + y2 + 6x + 6y + 9 = 0


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314.

The inverse point of (1, 2) with respect to the circle

x2 + y2 - 4x - 6y + 9 = 0 is

  • (0, 0)

  • (1, 0)

  • (0, 1)

  • (1, 1)


C.

(0, 1)

Iverse point of P (1, 2) w.r.t. the circle is the

foot ofthe perpendicular of P on the polar of P.

Given circle is x2 + y2 - 4x - 6y + 9 = 0

Polar of P(1, 2) is

x 1 + y 2 - 2x +1 - 3y +2 +9 = 0    x +2y - 2x - 2 - 3y - 6 + 9 = 0                                       x +y - 1 = 0Verifying inverse point of p is(0, 1)


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315.

The condition for the coaxial system x2 + y2 + 2λx + c = 0, where λ, is a parameter and c is a constant, to have distinct limiting points, is

  • c = 0

  • < 0

  • c = - 1

  • >


316.

For the parabola y2 + 6y - 2x + 5 = 0

(I) The vertex is (- 2, - 3)

(II) The directrix is y + 3 = 0

Which of the following is correct ?

  • Both I and II are true

  • I is true, II is false

  • I is false, II is true

  • Both I and II are false


317.

The value of k, If (1, 2), (k, - 1) are conjugate points with respect to the ellipse 2x2 + 3y2 = 6 is

  • 2

  • 4

  • 6

  • 8


318.

If the line lx + my = 1 is a normal to the hyperbola

x2a2 - y2b2 = 1, then a2l2 - b2m2 is equal to

  • a2 - b2

  • a2 + b2

  • (a2 + b2)2

  • (a2 - b2)2


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319.

If the lines 2x - 3y = 5 and 3x - 4y = 7 are two diameters of a circle of radius 7, then the equation of the circle is

  • x2 + y2 + 2x - 4y - 47 = 0

  • x2 + y2 = 49

  • x2 + y2 - 2x + 2y - 47 = 0

  • x2 + y2 = 17


320.

The inverse of the point (1, 2) with respect to the circle   

x2 + y2 - 4x - 6y + 9 = 0, is

  • 1, 12

  • 2, 1

  • 0, 1

  • 1, 0


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