Download App

STD 11 - 10.1 circle and system of circle — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 10.1 circle and system of circle4 Marks
MCQ
The minimum distance between any two points $P _{1}$ and $P _{2}$ while considering point $P _{1}$ on one circle and point $P _{2}$ on the other circle for the given circles' equations

$x^{2}+y^{2}-10 x-10 y+41=0$

$x^{2}+y^{2}-24 x-10 y+160=0$ is .........

  • A
    $4$
  • B
    $3$
  • C
    $2$
  • ✓
    $1$
✓

Answer

Correct option: D.
$1$
d
Given $C_{1}(5,5), r_{1}=3$ and $C_{2}(12,5), r_{2}=3$

Now, $C_{1} C_{2}>r_{1}+r_{2}$

Thus, $\left(P_{1} P_{2}\right)_{\min }=7-6=1$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$A$ and $B$ are two independent events. The probability that both $A$ and $B$ occur is $\frac{1}{6}$ and the probability that neither of them occurs is $\frac{1}{3}$. Then the probability of the two events are respectively
→
Position of the point $(1, 1)$ with respect to the circle ${x^2} + {y^2} - x + y - 1 = 0$ is
→
If $f(x)=\int_0^x e^{t^2}(t-2)(t-3) d t$ for all $x \in(0, \infty)$, then

$(A)$ $f$ has a local maximum at $x=2$

$(B)$ $f$ is decreasing on $(2,3)$

$(C)$ there exists some $c \in(0, \infty)$ such that $f ^{\prime \prime}( c )=0$

$(D)$ $f$ has a local minimum at $x=3$

→
${{{x^2} + 13x + 15} \over {(2x + 3)\,{{(x + 3)}^2}}} = $
→
If ${\log _7}2 = m,$ then ${\log _{49}}28$ is equal to
→
A tangent to the parabola ${y^2} = 8x$ makes an angle of ${45^o}$ with the straight line $y = 3x + 5$, then the equation of tangent is
→
If $A=\left(\begin{array}{cc}\frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}}\end{array}\right), B=\left(\begin{array}{ll}1 & 0 \\ i & 1\end{array}\right), i=\sqrt{-1}$, and

$\mathrm{Q}=\mathrm{A}^{\mathrm{T}} \mathrm{BA}$, then the inverse of the matrix $\mathrm{A} \mathrm{Q}^{2021} \mathrm{~A}^{\mathrm{T}}$ is equal to :

→
In an ellipse $9{x^2} + 5{y^2} = 45$, the distance between the foci is
→
The probability that a marksman will hit a target is given as $1/5$. Then his probability of at least one hit in $10$ shots, is
→
The sum of all two digit positive numbers which when divided by $7$ yield $2$ or $5$ as remainder is
→