Question
Find the equation of the circle with centre $\left( \frac { 1 } { 2 } , \frac { 1 } { 4 } \right)$ and radius $\frac { 1 } { 12 }$.
✓
Answer
Given centre is $\left( \frac { 1 } { 2 } , \frac { 1 } { 4 } \right)$
$\therefore$ h = $\frac { 1 } { 2 }$, k = $\frac { 1 } { 4 }$ and radius, r = $\frac { 1 } { 12 }$
On putting these values in equation of circle
$(x-h)^2+(y-k)^2=r^2 \text {, we get }$
$\left(x-\frac{1}{2}\right)^2+\left(y-\frac{1}{4}\right)^2=\left(\frac{1}{12}\right)^2$
$\Rightarrow x^2+\frac{1}{4}-x+y^2+\frac{1}{16}-\frac{y}{2}=\frac{1}{144}$
$\Rightarrow x^2+y^2-x-\frac{y}{2}+\frac{1}{4}+\frac{1}{16}-\frac{1}{144}=0$
$\Rightarrow x^2+y^2-x-\frac{y}{2}+\frac{11}{36}=0$
$\Rightarrow 36 x^2+36 y^2-36 x-18 y+11=0$
which is the required equation of circle.
$\therefore$ h = $\frac { 1 } { 2 }$, k = $\frac { 1 } { 4 }$ and radius, r = $\frac { 1 } { 12 }$
On putting these values in equation of circle
$(x-h)^2+(y-k)^2=r^2 \text {, we get }$
$\left(x-\frac{1}{2}\right)^2+\left(y-\frac{1}{4}\right)^2=\left(\frac{1}{12}\right)^2$
$\Rightarrow x^2+\frac{1}{4}-x+y^2+\frac{1}{16}-\frac{y}{2}=\frac{1}{144}$
$\Rightarrow x^2+y^2-x-\frac{y}{2}+\frac{1}{4}+\frac{1}{16}-\frac{1}{144}=0$
$\Rightarrow x^2+y^2-x-\frac{y}{2}+\frac{11}{36}=0$
$\Rightarrow 36 x^2+36 y^2-36 x-18 y+11=0$
which is the required equation of circle.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Show that the sequence defined by $\text{a}_\text{n}=\frac{2}{3^\text{n}},\text{n}\in\text{N}$ is a G.P.
→How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
Consider the following population and year graph: Find the slope of the line AB and using it, find what will be the population in the year 2010.
In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.
Find the coordinates of focus, axis, the equation of directrix and latus rectum of parabola $\mathrm{y}^2=8 \mathrm{x}$.
→Find the value of the following trigonomentric ratio: $\tan\Big(-\frac{13\pi}{4}\Big)$
→Compute: $\frac{30!}{28!}$
→Find the equation of the circle whose centre lies on the positive direction of y-axis at a distance 6 from the origin and whose radius is 4.
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
Show the following quadratic equation by factorization method: $x^2 + x + 1 = 0$
→