(B) The given equation of the circle is $x^2+y^2+2x+2y-3=0$. Completing the square,we get $(x+1)^2+(y+1)^2=5$. This is a circle with center $C(-1, -1)

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

(B) The given equation of the circle is $x^2+y^2+2x+2y-3=0$. Completing the square,we get $(x+1)^2+(y+1)^2=5$. This is a circle with center $C(-1, -1)$ and radius $r = \sqrt{5}$. The distance $d$ from the center $C(-1, -1)$ to the line $2x+y+13=0$ is given by $d = \frac{|2(-1) + (-1) + 13|}{\sqrt{2^2 + 1^2}} = \frac{|-2-1+13|}{\sqrt{5}} = \frac{10}{\sqrt{5}} = 2\sqrt{5}$. The maximum distance of a point on the circle from the line is $d + r$. Thus,$\lambda_{max} = 2\sqrt{5} + \sqrt{5} = 3\sqrt{5}$.

Class 11 Mathematics 10-1.Circle and System of Circles Geometrical problems regarding circle and its properties

Medium

If $\lambda$ is the perpendicular distance of a point $P$ on the circle $x^2+y^2+2x+2y-3=0$ from the line $2x+y+13=0$,then the maximum possible value of $\lambda$ is

MHT CET 2023 All MHT CET

A
$2 \sqrt{5}$
B
$3 \sqrt{5}$
C
$4 \sqrt{5}$
D
$\sqrt{5}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

10-1.Circle and System of Circles

Subtopic

Geometrical problems regarding circle and its properties

Previous Year

MHT CET 2023 Paper All MHT CET years →

Let $R$ be the region of the disc $x^2+y^2 \leq 1$ in the first quadrant. Then,the area of the largest possible circle contained in $R$ is

KVPY 2017

View Solution

In the figure,$ABCD$ is a unit square. $A$ circle is drawn with centre $O$ on the extended line $CD$ and passing through $A$. If the diagonal $AC$ is tangent to the circle,then the area of the shaded region is

KVPY 2017

View Solution

Two circles of radii $4 \text{ cm}$ and $1 \text{ cm}$ touch each other externally and $\theta$ is the angle contained by their direct common tangents. Then $\sin \theta =$

View Solution

If $(1, a)$ and $(b, 2)$ are conjugate points with respect to the circle $x^2+y^2=25$,then $4a+2b=$

DifficultTS EAMCET 2004

View Solution

If a circle $C$ passing through $(4, 0)$ touches the circle $x^2 + y^2 + 4x - 6y - 12 = 0$ externally at a point $(1, -1),$ then the radius of the circle $C$ is

DifficultJEE MAIN 2013

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If $\lambda$ is the perpendicular distance of a point $P$ on the circle $x^2+y^2+2x+2y-3=0$ from the line $2x+y+13=0$,then the maximum possible value of $\lambda$ is

Similar Questions

Let $R$ be the region of the disc $x^2+y^2 \leq 1$ in the first quadrant. Then,the area of the largest possible circle contained in $R$ is

In the figure,$ABCD$ is a unit square. $A$ circle is drawn with centre $O$ on the extended line $CD$ and passing through $A$. If the diagonal $AC$ is tangent to the circle,then the area of the shaded region is

Two circles of radii $4 \text{ cm}$ and $1 \text{ cm}$ touch each other externally and $\theta$ is the angle contained by their direct common tangents. Then $\sin \theta =$

If $(1, a)$ and $(b, 2)$ are conjugate points with respect to the circle $x^2+y^2=25$,then $4a+2b=$

If a circle $C$ passing through $(4, 0)$ touches the circle $x^2 + y^2 + 4x - 6y - 12 = 0$ externally at a point $(1, -1),$ then the radius of the circle $C$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module