Advertisements
Advertisements
प्रश्न
If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b). Prove that bx = ay.
Advertisements
उत्तर
P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b).
∴ AP = BP
∴ `sqrt([x-(a+b)]^2+[y-(b-a)]^2)=sqrt([x-(a-b)]^2+[y-(a+b)]^2`
∴ [x-(a+b)]2+[y-(b-a)]2 = [x-(a-b)]2+[y-(a+b)]2
∴ x2-2x(a+b)+(a+b)2+y2-2y(b-a)+(b-a)2
= x2-2x(a-b)+(a-b)2+y2-2y(a+b)+(a+b)2
∴ -2x(a+b)-2y(b-a)=-2x(a-b)-2y(a+b)
∴ ax+bx+by-ay=ax-bx+ay+by
∴ 2bx=2ay
∴bx=ay ...(proved)
APPEARS IN
संबंधित प्रश्न
If P (2, – 1), Q(3, 4), R(–2, 3) and S(–3, –2) be four points in a plane, show that PQRS is a rhombus but not a square. Find the area of the rhombus
Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).
Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.
Prove that the points A(1, 7), B (4, 2), C(−1, −1) D (−4, 4) are the vertices of a square.
P and Q are two points lying on the x - axis and the y-axis respectively . Find the coordinates of P and Q if the difference between the abscissa of P and the ordinates of Q is 1 and PQ is 5 units.
In what ratio does the point P(−4, y) divides the line segment joining the points A(−6, 10) and B(3, −8)? Hence find the value of y.
If the point (x, y) is at equidistant from the point (a + b, b – a) and (a-b, a + b). Prove that ay = bx.
Show that A(1, 2), (1, 6), C(1 + 2 `sqrt(3)`, 4) are vertices of a equilateral triangle
Seg OA is the radius of a circle with centre O. The coordinates of point A is (0, 2) then decide whether the point B(1, 2) is on the circle?
The distance between the points A(0, 6) and B(0, –2) is ______.
