Tag: midpoints

Question 1

Multiple choice maths constructions mid-point formula midpoints division of a line segment

The locus of the mid point of the portion intercepted between the axes by the line $x{\,}cos\alpha+y{\,}sin{\,} \alpha=p$, where $p\inR$, is

$\dfrac{1}{x^2}+\dfrac{1}{y^2}=\dfrac{4}{p^2}$
$\dfrac{1}{x^2}-\dfrac{1}{y^2}=\dfrac{4}{p^2}$
$\dfrac{1}{x^2}+\dfrac{1}{y^2}=\dfrac{2}{p^2}$

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Answer

$x^2+y^2=\dfrac{4}{p^2}$

Question 2

Multiple choice maths constructions mid-point formula midpoints division of a line segment

Locus of the midpoints of the intercepts between the co-ordinate Axes by the lines passing through (a, 0) does not intersect

X axis
Y axis
Y=x
Y=a

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Answer

$a _{1}^{2}+b _{1}^{2}+a _{2}^{2}+b _{2}^{2}$

Answer

x+y=2, x+y=3

Answer

$x^{2}=4y$

Answer

$\dfrac{-3}{2}$

Answer

$\frac{1}{x^{2}}+\frac{1}{y^{2}}=\frac{1}{a^{2}}$

Answer

$(2, 3, 5)$

Answer

$x + y = 2$

Question 3

Multiple choice maths constructions mid-point formula midpoints division of a line segment

If the $1st$ point of trisection of AB is $(t, 2t)$ and the ends A, B move on $x$ and $y$ axis respectfully, then the focus of midpoint of AB is

$x=y$
$2x= y$
$4x= y$
$x= 4y$

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Question 4

Multiple choice maths constructions mid-point formula midpoints division of a line segment

I every points on the line $(a _{1}-a _{2})x+(b _{1}-b _{2}),y=c$ is equidistance from the points $(a _{1},b _{1})$ and $(a _{2},b _{2})$ then $2c=$

$a _{1}^{2}-b _{1}^{2}+a _{2}^{2}-b _{2}^{2}$
$a _{1}^{2}+b _{1}^{2}-a _{2}^{2}-b _{2}^{2}$
$None\ of\ these$

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Question 5

Multiple choice maths constructions mid-point formula midpoints division of a line segment

The line equally inclined to the coordinates axes and equidistant from points A(1, -2) and B(3, 4) is

x-y=3, x-y=1
x-y=1, x+y=3
x+y=2, x-y=3

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Question 6

Multiple choice maths constructions mid-point formula midpoints division of a line segment

Let $O$ be the origin and $A$ be a point on the curve $y^{2}=4x$. then locus of midpoint of $OA$ is

$x^{2}=4y$
$y^{2}=16x$
$y^{2}=2x$

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Question 7

Multiple choice maths constructions mid-point formula midpoints division of a line segment

The midpoint of the interval in which $x^{2}-2(\sqrt{-x})^{2}-3<0$ is satisfied, is

$-2$
$\dfrac{1}{2}$
$\dfrac{-3}{4}$

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Question 8

Multiple choice maths constructions mid-point formula midpoints division of a line segment

A tangent to the circle $x^{2}+y^{2}=a^{2}$ meets the axes at points A and B. The locus of the mid point of AB is

$\frac{1}{x^{2}}+\frac{1}{y^{2}}=\frac{4}{a^{2}}$
$\frac{1}{x^{2}}+\frac{1}{y^{2}}=4a^{2}$
$\frac{1}{x^{2}}+\frac{1}{y^{2}}=\frac{a^{2}}{4}$

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Question 9

Multiple choice maths constructions mid-point formula midpoints division of a line segment

If $A=(1, 2, 3)$ and $B(3, 5, 7)$ and P, Q are the points on AB such that AP$=$PQ$\neq$QB, then the mid point of PQ is?

$\left(2, \dfrac{7}{2}, 5\right)$
$(2, 4, 5)$
$(4, 7, 0)$

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Question 10

Multiple choice maths constructions mid-point formula midpoints division of a line segment

The locus of the mid-point of a chord of the circle ${ x }^{ 2 }+{ y }^{ 2 }=4$ which subtends a right angle at the origin, is

$x^2 + y^2 = 1$
$x^2 + y^2 = 2$
$x + y = 1$

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