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Maths-

General

Easy

Question

Two fixed points A and B are taken on the rectangular coordinate axes such that OA = a and OB =b Two variable points P and Q are taken on the same axes so that OP+OQ=OA+OB The locus of the intersection of AQ and BP is

x‐y $=$ a
x+y=a+b
x‐y =b- a
x‐y =b

The correct answer is: x+y=a+b

Let $O P equals a to the power of 1 end exponent comma O Q equals b to the power of ’ end exponent rightwards double arrow a minus a to the power of 1 end exponent equals b minus b to the power of ’ end exponent$ given
equation of $A Q colon fraction numerator x over denominator a end fraction plus fraction numerator y over denominator b to the power of ’ end exponent end fraction equals 1 semicolon$ of $P B colon fraction numerator x over denominator a end fraction plus fraction numerator y over denominator b end fraction ’ equals 1 rightwards double arrow fraction numerator x over denominator a a end fraction plus fraction numerator y over denominator b b to the power of ’ end exponent end fraction ’ equals 0$ (using given)
also $fraction numerator x over denominator a b end fraction plus fraction numerator y over denominator b to the power of ’ end exponent end fraction equals fraction numerator 1 over denominator b end fraction comma fraction numerator x over denominator a a end fraction plus fraction numerator y over denominator a b end fraction ’ equals fraction numerator 1 over denominator a end fraction rightwards double arrow fraction numerator x plus y over denominator a b end fraction equals fraction numerator a plus b over denominator a b end fraction$

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M is the midpoint of side AB of equilateral triangle ABC p is a point on BC such that AP+PM is minimum If AB =20 then the value of AP +PM is

M is the midpoint of side AB of equilateral triangle ABC p is a point on BC such that AP+PM is minimum If AB =20 then the value of AP +PM is

If the line $y equals x square root of 3$ cuts the curve $x to the power of 3 end exponent plus y to the power of 3 end exponent plus 3 x y plus 5 x to the power of 2 end exponent plus 3 y to the power of 2 end exponent plus 4 x plus 5 y minus 1 equals 0$ at the points A,B and $C$ then OA.OB.OC =-( where O is origin)

If the line $y equals x square root of 3$ cuts the curve $x to the power of 3 end exponent plus y to the power of 3 end exponent plus 3 x y plus 5 x to the power of 2 end exponent plus 3 y to the power of 2 end exponent plus 4 x plus 5 y minus 1 equals 0$ at the points A,B and $C$ then OA.OB.OC =-( where O is origin)

$a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent plus 2 g x plus 2 f y plus c equals 0$ represent two parallel lines if

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parallel

In $capital delta A B C comma$ $P$ is any point inside a triangle such that area of $capital delta B P C comma$ $capital delta A P C comma$ $capital delta A P B$ are equal Line AP cut BC at $M$ , area of $capital delta P M C$ is 5 $s q$ unit then area of $capital delta A B C$ is

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$a to the power of 2 end exponent cos to the power of 2 end exponent invisible function application fraction numerator 2 pi over denominator 3 end fraction minus 4 a to the power of 2 end exponent tan to the power of 2 end exponent invisible function application fraction numerator 3 pi over denominator 4 end fraction plus 2 a to the power of 2 end exponent sin to the power of 2 end exponent invisible function application fraction numerator 2 pi over denominator 3 end fraction equals$

$a to the power of 2 end exponent cos to the power of 2 end exponent invisible function application fraction numerator 2 pi over denominator 3 end fraction minus 4 a to the power of 2 end exponent tan to the power of 2 end exponent invisible function application fraction numerator 3 pi over denominator 4 end fraction plus 2 a to the power of 2 end exponent sin to the power of 2 end exponent invisible function application fraction numerator 2 pi over denominator 3 end fraction equals$

In a right angled triangle ABC, $stack C with _ below equals 90 to the power of ring operator end exponent text , end text$ then $cos to the power of 2 end exponent invisible function application A plus cos to the power of 2 end exponent invisible function application B equals$

In a right angled triangle ABC, $stack C with _ below equals 90 to the power of ring operator end exponent text , end text$ then $cos to the power of 2 end exponent invisible function application A plus cos to the power of 2 end exponent invisible function application B equals$

parallel

If $cos invisible function application theta subscript 1 end subscript plus cos invisible function application theta subscript 2 end subscript plus cos invisible function application theta subscript 3 end subscript plus cos invisible function application theta subscript 4 end subscript plus cos invisible function application theta subscript 5 end subscript equals 5$ then $sin invisible function application theta subscript 1 end subscript plus sin invisible function application theta subscript 2 end subscript plus sin invisible function application theta subscript 3 end subscript plus sin invisible function application theta subscript 4 end subscript plus sin invisible function application theta subscript 5 end subscript equals$

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parallel

If $cos invisible function application open parentheses x minus y close parentheses equals negative 1$ , then $cos invisible function application x plus cos invisible function application y equals$

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parallel

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parallel

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