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GradeDistance Formula, Distance Formula

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Find a point on the x axis which is equidistant from the point $A(2,-5)$ and $B(-2,9)$.

Show that $(3,2),\,\,(2, - 3),\,\,(0,0)$ are the vertices of a right- angled triangle using the distance formula.

If a point \[P\left( {x,y} \right)\] is equidistant from the points \[A\left( {6, - 1} \right)\] and \[B\left( {2,3} \right)\] , find the relation between x and y.

What is the distance between the origin and the point $\left( { - 19,6} \right)$ ?

Points A \[(-1,y)\] and B \[(5,7)\] lie on a circle with center O \[(2,-3y)\]. find the values of y. Hence, find the radius of the circle.

Given $ABCD$ is a rectangle with $B\left( -5,0 \right),C\left( 7,0 \right)$ and $D\left( 7,3 \right)$ . What is the coordinate of $A$ ?

Find all possible values of \[y\] for which the distance between the points \[A(2, - 3)\] and \[B(10,y)\] is \[10\] units.

Show that \[A( - 3,2)\], \[B( - 5, - 5)\], \[C(2, - 3)\] and \[D(4,4)\] are the vertices of a rhombus.

Find all possible values of $x$ for which the distance between the points $A\left( x,-1 \right)$ and $B\left( 5,3 \right)$ is $5$ units.

Find the coordinates of a point on \[y - axis\] which are at a distance of \[5\sqrt 2 \] from the point \[P\left( {3, - 2,5} \right)\] .

What is the equation of the locus of a point which moves such that 4 times its distance from the x-axis is the square of its distance from the origin?

a). ${x^2} + {y^2} - 4y = 0$

b). ${x^2} + {y^2} - 4|y| = 0$

c). ${x^2} + {y^2} - 4x = 0$

d). ${x^2} + {y^2} - 4|x| = 0$

a). ${x^2} + {y^2} - 4y = 0$

b). ${x^2} + {y^2} - 4|y| = 0$

c). ${x^2} + {y^2} - 4x = 0$

d). ${x^2} + {y^2} - 4|x| = 0$

If the distance of the point P from A(6,0) is twice its distance from the point B(1,3), prove that the locus of the point P is a circle . Also find its center and its radius.

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