P(3,1),Q(6,5) and R(x,y) are three points suc | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Since $\angle PRQ = 90^{\circ}$,the point $R$ must lie on a circle with $PQ$ as its diameter.The length of the diameter $PQ = \sqrt{(6-3)^2 + (5-1

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) Since $\angle PRQ = 90^{\circ}$,the point $R$ must lie on a circle with $PQ$ as its diameter.The length of the diameter $PQ = \sqrt{(6-3)^2 + (5-1)^2} = \sqrt{3^2 + 4^2} = \sqrt{9+16} = 5$.The radius of this circle is $r = \frac{5}{2} = 2.5$.The area of $\Delta RPQ = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = 5$.$\frac{1}{2} 	imes PQ 	imes h = 5 \implies \frac{1}{2} 	imes 5 	imes h = 5 \implies h = 2$.Here,$h$ is the perpendicular distance of point $R$ from the line segment $PQ$.Since the maximum height of any point on the circle from the diameter $PQ$ is the radius $r = 2.5$,and we require $h = 2$,there exist two points on the upper semi-circle and two points on the lower semi-circle that satisfy this condition.Thus,there are $4$ such points $R$.

$P(3,1)$,$Q(6,5)$ and $R(x,y)$ are three points such that the angle $\angle PRQ$ is a right angle and the area of the $\Delta RPQ = 5$. Then the number of such points $R$ is

Similar Questions

The equation of the circle which touches the coordinate axes and the line $\frac{x}{3} + \frac{y}{4} = 1$,and whose centre lies in the first quadrant,is ${x^2} + {y^2} - 2cx - 2cy + {c^2} = 0$,where $c$ is:

Find the angle of intersection of the two circles $x^2 + y^2 - 2x - 2y = 0$ and $x^2 + y^2 = 4$ in degrees.

Let $A(3,5)$,$B(-2,-7)$ and $C(\alpha, \beta)$ be three points such that $\angle ACB$ is a right angle and the area of triangle $ABC$ is $\frac{82}{3}$ square units. Then the number of such points $C$ is

If $A=(0,-2)$ and $B$ is any point on the circle $x^2+y^2-2x-2y+1=0$,then the maximum value of $(AB)^2$ is

The length of the intercept that the circle $x^2 + y^2 + 10x - 6y + 9 = 0$ makes on the $x$-axis is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module