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Maths-

General

Easy

Question

Consider the circles, $S subscript 1 end subscript colon x to the power of 2 end exponent plus y to the power of 2 end exponent plus 2 x minus 4 equals 0$ and $S subscript 2 end subscript colon x to the power of 2 end exponent plus y to the power of 2 end exponent minus y plus 1 equals 0$
Statement‐I Tangents from the point P(O, 5) on $S subscript 1 end subscript$ and $S subscript 2 end subscript$ are equal
Statement‐II Point P(O, 5) lies on the radical axis of the two circles.

Statement‐I is true, Statement‐II is true ; Statement‐II is correct explanation for Statement‐I.
Statement‐I is true, Statement‐II is true ; Statement‐II is NOT a correct explanation for statement‐I.
Statement‐I is true, Statement‐II is false.
Statement‐I is false, Statement‐II is true.

The correct answer is: Statement‐I is true, Statement‐II is true ; Statement‐II is correct explanation for Statement‐I.

Related Questions to study

Statement‐I Angle between the tangents drawn from the point P(13,6) to the circle $S colon x to the power of 2 end exponent plus y to the power of 2 end exponent minus 6 x plus 8 y minus 75 equals 0$ is 90.
Statement‐II Point $P$ lies on the director circle of S.

Statement‐I Angle between the tangents drawn from the point P(13,6) to the circle $S colon x to the power of 2 end exponent plus y to the power of 2 end exponent minus 6 x plus 8 y minus 75 equals 0$ is 90.
Statement‐II Point $P$ lies on the director circle of S.

The common chord of two intersecting circles $C subscript 1 end subscript$ and $C subscript 2 end subscript$ can be seen from their centres at the angles of 90°& 60° respectively If the distance between their centres is equal to $square root of 3 plus 1$ then the radii of $C subscript 1 end subscript$ and $C subscript 2 end subscript$ are‐

The common chord of two intersecting circles $C subscript 1 end subscript$ and $C subscript 2 end subscript$ can be seen from their centres at the angles of 90°& 60° respectively If the distance between their centres is equal to $square root of 3 plus 1$ then the radii of $C subscript 1 end subscript$ and $C subscript 2 end subscript$ are‐

If the two circles, $x to the power of 2 end exponent plus y to the power of 2 end exponent plus 2 g subscript 1 end subscript x plus 2 f subscript 1 end subscript y equals 0$ and $x to the power of 2 end exponent plus y to the power of 2 end exponent plus 2 g subscript 2 end subscript x plus 2 f subscript 2 end subscript y equals 0$ touches each other, then‐

If the two circles, $x to the power of 2 end exponent plus y to the power of 2 end exponent plus 2 g subscript 1 end subscript x plus 2 f subscript 1 end subscript y equals 0$ and $x to the power of 2 end exponent plus y to the power of 2 end exponent plus 2 g subscript 2 end subscript x plus 2 f subscript 2 end subscript y equals 0$ touches each other, then‐

parallel

Pair of tangents are drawn from every point on the line 3x+4y=12 on the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 4$ Their variable chord of contact always passes through a fixed point whose co‐ordinates are ‐

Pair of tangents are drawn from every point on the line 3x+4y=12 on the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 4$ Their variable chord of contact always passes through a fixed point whose co‐ordinates are ‐

The locus of the centres of the circles which cut the circles $x to the power of 2 end exponent plus y to the power of 2 end exponent plus 4 x minus 6 y plus 9 equals 0$ and $x to the power of 2 end exponent plus y to the power of 2 end exponent minus 5 x plus 4 y minus 2 equals 0$ orthogonally is ‐

The locus of the centres of the circles which cut the circles $x to the power of 2 end exponent plus y to the power of 2 end exponent plus 4 x minus 6 y plus 9 equals 0$ and $x to the power of 2 end exponent plus y to the power of 2 end exponent minus 5 x plus 4 y minus 2 equals 0$ orthogonally is ‐

The centre of the smallest circle touching the circles $x squared plus y squared minus 2 y minus 3 equals 0$ and $x squared plus y squared minus 8 x minus 18 y plus 93 equals 0$ is

The centre of the smallest circle touching the circles $x squared plus y squared minus 2 y minus 3 equals 0$ and $x squared plus y squared minus 8 x minus 18 y plus 93 equals 0$ is

parallel

Statement -I : If – 2h = a + b, then one line of the pair of lines $a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent equals 0$ bisects the angle between co-ordinate axes in positive quadrant.
Statement -II : If ax + y(2h + a) = 0 is a factor of $a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent equals 0$ then b + 2h + a = 0.

Statement -I : If – 2h = a + b, then one line of the pair of lines $a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent equals 0$ bisects the angle between co-ordinate axes in positive quadrant.
Statement -II : If ax + y(2h + a) = 0 is a factor of $a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent equals 0$ then b + 2h + a = 0.

P is point on either of the two lines $y minus square root of 3 vertical line x vertical line equals 2$ at a distance of 5 units from their point of intersection. The co-ordinates of the foot of the perpendicular from P on the bisector of the angle between them are :-

P is point on either of the two lines $y minus square root of 3 vertical line x vertical line equals 2$ at a distance of 5 units from their point of intersection. The co-ordinates of the foot of the perpendicular from P on the bisector of the angle between them are :-

$alpha comma blank beta$ are the roots of the equation $x squared minus 3 x plus A equals 0$ and $gamma comma delta$ are the roots of the equation $x squared minus 12 x plus B equals 0. I f alpha comma beta comma gamma comma delta$ form an increasing GP, then $left parenthesis A comma blank B right parenthesis$ is equal to

$alpha comma blank beta$ are the roots of the equation $x squared minus 3 x plus A equals 0$ and $gamma comma delta$ are the roots of the equation $x squared minus 12 x plus B equals 0. I f alpha comma beta comma gamma comma delta$ form an increasing GP, then $left parenthesis A comma blank B right parenthesis$ is equal to

parallel

The sum of the series $1 times n plus 1 plus 2 times open parentheses n minus 1 close parentheses plus 3 times open parentheses n minus 2 close parentheses horizontal ellipsis plus n times 1$ is

The sum of the series $1 times n plus 1 plus 2 times open parentheses n minus 1 close parentheses plus 3 times open parentheses n minus 2 close parentheses horizontal ellipsis plus n times 1$ is

The sum of the series $1 times 2 times 3 plus 2 times 3 times 4 plus 3 times 4 times 5 plus...$ to $n$ terms is

The sum of the series $1 times 2 times 3 plus 2 times 3 times 4 plus 3 times 4 times 5 plus...$ to $n$ terms is

If the sum of an infinite GP and the sum of square of its term is 3, then the common ratio of the first series is

If the sum of an infinite GP and the sum of square of its term is 3, then the common ratio of the first series is

parallel

If $a$ and $b$ are two different positive real numbers, then which of the following relations is true

If $a$ and $b$ are two different positive real numbers, then which of the following relations is true

If $A subscript 1 end subscript comma blank A subscript 2 end subscript$ are two A $blank times$ M’s between $a$ and $b$ and $G subscript 1 end subscript comma blank G subscript 2 end subscript$ are two GM’s between $a$ and $b$ then $fraction numerator A subscript 1 end subscript plus A subscript 2 end subscript over denominator G subscript 1 end subscript G subscript 2 end subscript end fraction$ is

If $A subscript 1 end subscript comma blank A subscript 2 end subscript$ are two A $blank times$ M’s between $a$ and $b$ and $G subscript 1 end subscript comma blank G subscript 2 end subscript$ are two GM’s between $a$ and $b$ then $fraction numerator A subscript 1 end subscript plus A subscript 2 end subscript over denominator G subscript 1 end subscript G subscript 2 end subscript end fraction$ is

the sum of $n$ terms of the infinite series $1 times 3 squared plus 2 times 5 squared plus 3 times 7 squared plus... infinity$ is

the sum of $n$ terms of the infinite series $1 times 3 squared plus 2 times 5 squared plus 3 times 7 squared plus... infinity$ is

parallel

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