Full Name

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Address, City, State, Country

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Email Address

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The lines ax + by + c = 0 and px + qy + r = 0 cut the coordinate axes in con-cyclic points then:

ap + bq = 0
ap - bq = 0
ab + pq = 0
ab - pq = 0

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The two circles x^2 + y^2 + 2gx + 2fy = 0 and x^2 + y^2 + 2px + 2qy = 0 touch each other. This implies that,

fp = gq
fq = pg
f^2 + g^2 = p^2 + q^2
None of the options above hold(s) true

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The locus of a point from which tangents to two circles x^2 + y^2 - 5x - 3 = 0 and 3*x^2 + 3 *y^2 + 2x + 4y - 6 = 0 are equal, is:

2 * x^2 + 2 * y^2 + 7x + 4y -3 = 0
17x + 4y + 3 = 0
4 * x^2 + 4 * y^2 - 3x + 4y - 9 = 0
13x - 4y + 15 = 0

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The Locus of the point of intersection of the tangents to the circle x = r cos A, y = r sin A at points whose parametric angles differ by PI / 3 is :

x^2 + y^2 = 4 * ( 2 - sqrt(3)) * r * r
x^2 + y^2 = 1
x^2 + y^2 = ( 2 - sqrt(3)) * r * r
3 * ( x^2 + y^2 ) = 4 * (r ^ 2)

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X-coordinates of two points A and B are roots of the equation x^2 + 2ax - b^2 = 0 and the Y-coordinates are the roots of the equation x^2 + 2px - q^2 = 0

square_root(a^2 + b^2 + p^2 + q^2)
square_root(a^2 + p^2)
square_root(b^2 + q^2)
None of these options above

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Area of the triangle formed by the tangent at the point (u,v) of the circle (x^2 + y^2 = r^2 ) is :

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The squares of the lengths of the tangents to the circles x^2 + y^2 = a^2, x^2 + y^2 = b^2 and x^2 + y^2 = c^2 are in AP then a^2, b^2 and c^2 are in ...

Arithmetic Progression
Geometric Progression
Harmonic Progression
A mixed kind of progression/sequence

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AP and BQ are parallel tangents to a circle. A tangent at any point C cuts them at P and Q respectively. Is CP.CQ independent of the point C?

Yes
No
Insufficient data to decide.

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Let A be the center of the circle x^2 + y^2 -2x -4y - 20 = 0. The tangents to this circle at the points B(1,7) and D(4,-2) meet at C. What is the Area of the Quadrilateral ABCD ?

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Consider the circle x^2 + y^2 + 4x - 4y + 4 = 0. Does this touch the coordinate axes?

Yes
No

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MCQ Quiz- Mathematics- Coordinate Geometry: The Circle - Test III