Advertisements
Advertisements
प्रश्न
Find the distance between the points
P(a sin ∝,a cos ∝ )and Q( acos ∝ ,- asin ∝)
उत्तर
P( a sin ∝,a cos ∝ ) and Q(a cos a ,- a sin ∝)
The given points are P( a sin ∝,a cos ∝ ) and Q(a cos a ,- a sin ∝)
`Then (x_1 = a sin , y_1 = a cos ∝ ) and (x_2 = a cos a , y_2 = - a sin ∝ )`
`PQ = sqrt( (x_2 -x_1)^2 + (y_2-y_1)^2)`
`= sqrt(( a cos ∝ - a sin ∝ )^2 + ( -a sin ∝ - a cos ∝ )^2)`
`=sqrt((a^2 cos^2 ∝ + a^2 sin^2 ∝ - 2a^2 cos ∝ xx sin ∝ )+(a^2 sin^2 ∝ + a^2 cos^2 ∝ +2a^2 cos ∝ xx sin ∝ ))`
`= sqrt(2a^2 cos^2 ∝ +2a^2 sin^2 ∝ )`
`= sqrt(2a^2 (cos^2 ∝ + sin^2 ∝ ))`
`= sqrt( 2a^2 (1)) ("From the identity" cos^2 ∝ + sin^2 ∝=1 )`
`=sqrt(2a^2)`
`= sqrt(2a)` units
APPEARS IN
संबंधित प्रश्न
If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.
Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area
Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.
Find the distance between the following pair of points:
(asinα, −bcosα) and (−acos α, bsin α)
Find the distance between the following pair of points.
R(0, -3), S(0, `5/2`)
Find the distance between the following point :
(p+q,p-q) and (p-q, p-q)
Prove that the points (1 ,1),(-4 , 4) and (4 , 6) are the certices of an isosceles triangle.
Find the distance between the points (a, b) and (−a, −b).
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 distance between point L(x, 7) and point M(1, 15) is 10, then find the value of x
