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Question

From a point R(5, 8) two tangents RP and RQ are drawn to a given circle S = 0 whose radius is 5. If circumcentre of the triangle PQR is (2, 3), then the equation of circle S = 0 is

$x^{2} + y^{2} + 2 x + 4 y - 20 = 0$
$x^{2} + y^{2} + x + 2 y - 10 = 0$
$x^{2} + y^{2} - x - 2 y - 20 = 0$
$x^{2} + y^{2} - 4 x - 6 y - 12 = 0$

The correct answer is: $x to the power of 2 end exponent plus y to the power of 2 end exponent plus 2 x plus 4 y minus 20 equals 0$

Related Questions to study

PA and PB are tangents to a circle S touching S at points A and B.C is a point on S in between A and B as shown in the figure. LCM is a tangent to S intersecting PA and PB in points L and M respectively.Then the perimeter of the triangle PLM depends on

PA and PB are tangents to a circle S touching S at points A and B.C is a point on S in between A and B as shown in the figure. LCM is a tangent to S intersecting PA and PB in points L and M respectively.Then the perimeter of the triangle PLM depends on

$left parenthesis 1 , 2 square root of 2 right parenthesis$ is a point on circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 9$ locate the points on the given circle which are at 2 unit distance from $left parenthesis 1 , 2 square root of 2 right parenthesis$

$left parenthesis 1 , 2 square root of 2 right parenthesis$ is a point on circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 9$ locate the points on the given circle which are at 2 unit distance from $left parenthesis 1 , 2 square root of 2 right parenthesis$

In the adjoining figure, the circle meets the sides of an equilateral triangle at six points. If Ag = 2, GF = 13, FC = 1 and HJ = 7, then DE equals

In the adjoining figure, the circle meets the sides of an equilateral triangle at six points. If Ag = 2, GF = 13, FC = 1 and HJ = 7, then DE equals

parallel

If a line segment AM = a moves in the plane XOY remaining parallel to OX so that the left end point A slides along the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals a to the power of 2 end exponent comma text the locus of end text M text is end text$

If a line segment AM = a moves in the plane XOY remaining parallel to OX so that the left end point A slides along the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals a to the power of 2 end exponent comma text the locus of end text M text is end text$

The triangle PQR is inscribed in the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 25 text . end text$ If Q and R have coordinates (3, 4) and (-4, 3) respectively, then $angle Q P R$ is

The triangle PQR is inscribed in the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 25 text . end text$ If Q and R have coordinates (3, 4) and (-4, 3) respectively, then $angle Q P R$ is

For all values of m ÎR the line y-mx + m-1 = 0 cuts the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent minus 2 x minus 2 y plus 1 equals 0 text end text$ at an angle

For all values of m ÎR the line y-mx + m-1 = 0 cuts the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent minus 2 x minus 2 y plus 1 equals 0 text end text$ at an angle

parallel

$C subscript 1 end subscript$ is a circle of radius 1 touching the x -axis and y -axis. $text end text C subscript 2 end subscript$ is another circle of radius $greater than 1$ and touching the axes as well as circle $C subscript 1 end subscript. text Then the radius of end text C subscript 2 end subscript text end text text is end text$

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PA and PB are tangents to a circle S touching S at points A and B.C is a point on S in between A and B as shown in the figure. LCM is a tangent to S intersecting PA and PB in points L and M respectively.Then the perimeter of the triangle PLM depends on

PA and PB are tangents to a circle S touching S at points A and B.C is a point on S in between A and B as shown in the figure. LCM is a tangent to S intersecting PA and PB in points L and M respectively.Then the perimeter of the triangle PLM depends on

The centres of two circles are $5 square root of 2$ units apart. The circles are orthogonal and their radii are integers $not equal to$ 1. The area of the region, in square units, common to the two circles, is

The centres of two circles are $5 square root of 2$ units apart. The circles are orthogonal and their radii are integers $not equal to$ 1. The area of the region, in square units, common to the two circles, is

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If two chords, each bisected by the x - axis can be drawn to the circle, $2 open parentheses x to the power of 2 end exponent plus y to the power of 2 end exponent close parentheses minus 2 a x minus b y equals 0 left parenthesis a not equal to 0 comma b not equal to 0 right parenthesis text end text$ from the point $text end text left parenthesis a comma b divided by 2 right parenthesis text end text$ then :

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The radius of the least circle passing through the point (8, 4) and cutting the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 40$ orthogonally is

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P(3,2) is a point on the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 13$ Two points A, B are on the circle such that $P A equals P B equals square root of 5$ The equation of chord AB is

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parallel

Statement – 1: Two circles of radii $square root of 3 & 1$ cut orthogonally then area of common region is $fraction numerator 5 pi minus 6 square root of 3 over denominator 6 end fraction$ square unit.
Statement -2: Area $text end text left parenthesis A union B right parenthesis equals text AreaA end text plus text Area end text left parenthesis B right parenthesis minus text Area end text left parenthesis A intersection B right parenthesis$ , where A & B represents two regions

Statement – 1: Two circles of radii $square root of 3 & 1$ cut orthogonally then area of common region is $fraction numerator 5 pi minus 6 square root of 3 over denominator 6 end fraction$ square unit.
Statement -2: Area $text end text left parenthesis A union B right parenthesis equals text AreaA end text plus text Area end text left parenthesis B right parenthesis minus text Area end text left parenthesis A intersection B right parenthesis$ , where A & B represents two regions

Statement (I) : 27, 8 and 12 can be three terms of G.P. as well as an A.P
Statement (II) : Three non-zero real numbers can always be three terms of an A.P

Statement (I) : 27, 8 and 12 can be three terms of G.P. as well as an A.P
Statement (II) : Three non-zero real numbers can always be three terms of an A.P

The value of $blank to the power of n end exponent C subscript 1 end subscript minus open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction close parentheses blank to the power of n end exponent C subscript 2 end subscript plus open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction close parentheses blank to the power of n end exponent C subscript 3 end subscript minus horizontal ellipsis horizontal ellipsis horizontal ellipsis. plus left parenthesis negative 1 right parenthesis to the power of n minus 1 end exponent open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus horizontal ellipsis horizontal ellipsis horizontal ellipsis times fraction numerator 1 over denominator n end fraction close parentheses blank to the power of n end exponent C subscript n end subscript text is end text$

The value of $blank to the power of n end exponent C subscript 1 end subscript minus open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction close parentheses blank to the power of n end exponent C subscript 2 end subscript plus open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction close parentheses blank to the power of n end exponent C subscript 3 end subscript minus horizontal ellipsis horizontal ellipsis horizontal ellipsis. plus left parenthesis negative 1 right parenthesis to the power of n minus 1 end exponent open parentheses 1 plus fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction plus horizontal ellipsis horizontal ellipsis horizontal ellipsis times fraction numerator 1 over denominator n end fraction close parentheses blank to the power of n end exponent C subscript n end subscript text is end text$

parallel

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