(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 →

The lengths of the tangents from the point $(1,2)$ to the circles $x^2+y^2+x+y-4=0$ and $3x^2+3y^2-x-y-k=0$ are in the ratio $4:3$. Then the value of $k$ is:

EasyAP EAMCET 2021

View Solution

The points $(x_1, y_1), (x_2, y_2), (x_1, y_2),$ and $(x_2, y_1)$ are always:

View Solution

Chords $AB$ and $CD$ of a circle intersect at a right angle at point $P$. If the lengths of $AP$, $PB$, $CP$, and $PD$ are $2$, $6$, $3$, and $4$ units respectively, then the radius of the circle is:

EasyWBJEE 2024

View Solution

Match the statements in Column $I$ with the properties in Column $II$.

Column $I$ Column $II$

$(A)$ Two intersecting circles $(p)$ have a common tangent

$(B)$ Two mutually external circles $(q)$ have a common normal

$(C)$ Two circles,one strictly inside the other $(r)$ do not have a common tangent

$(D)$ Two branches of a hyperbola $(s)$ do not have a common normal

DifficultIIT 2007

View Solution

If the line $y - 1 = m(x - 1)$ intersects the circle $x^2 + y^2 = 4$ at two distinct points,then the number of possible values of $m$ is:

Medium

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

Column $I$	Column $II$
$(A)$ Two intersecting circles	$(p)$ have a common tangent
$(B)$ Two mutually external circles	$(q)$ have a common normal
$(C)$ Two circles,one strictly inside the other	$(r)$ do not have a common tangent
$(D)$ Two branches of a hyperbola	$(s)$ do not have a common normal

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

The lengths of the tangents from the point $(1,2)$ to the circles $x^2+y^2+x+y-4=0$ and $3x^2+3y^2-x-y-k=0$ are in the ratio $4:3$. Then the value of $k$ is:

The points $(x_1, y_1), (x_2, y_2), (x_1, y_2),$ and $(x_2, y_1)$ are always:

Chords $AB$ and $CD$ of a circle intersect at a right angle at point $P$. If the lengths of $AP$, $PB$, $CP$, and $PD$ are $2$, $6$, $3$, and $4$ units respectively, then the radius of the circle is:

If the line $y - 1 = m(x - 1)$ intersects the circle $x^2 + y^2 = 4$ at two distinct points,then the number of possible values of $m$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module