Register

ISI2014-DCG-60

• recategorized by
504 views
1 votes
1 votes

The equation of any circle passing through the origin and with its centre on the $X$-axis is given by

  1. $x^2+y^2-2ax=0$ where $a$ must be positive
  2. $x^2+y^2-2ax=0$ for any given $a \in \mathbb{R}$
  3. $x^2+y^2-2by=0$ where $b$ must be positive
  4. $x^2+y^2-2by=0$ for any given $b \in \mathbb{R}$
• recategorized by
User Avatar

1 Answer

1 votes
1 votes
Answer: $\mathbf A$

If a circle passes through the origin and the centre lies on the $\mathrm x$ axis then the length of the abscissa will be equal to the circle's radius and the ordinate(y-coordinate) will be $0$.

So, the equation of the circle will be of the form:

$\mathrm {(x-a)^2 + y^2 = a^2}$

$\Rightarrow \mathrm{ x^2 + y^2 -2ax = 0}$

$\therefore \mathbf A $ is the right option.
User Avatar
Voting & Accepting an answer helps improve the community
← PreviousNext →
← Previous in categoryNext in category →

Related questions

2 votes
2 votes
1 answer
1
Arjun asked Sep 23, 2019
515 views
ISI2014-DCG-58
Consider a circle with centre at origin and radius $2\sqrt{2}$. A square is inscribed in the circle whose sides are parallel to the $X$ an $Y$ axes. The coordinates of one of the vertices of this square are $(2, -2)$ $(2\sqrt{2},-2)$ $(-2, 2\sqrt{2})$ $(2\sqrt{2}, -2\sqrt{2})$
Consider a circle with centre at origin and radius $2\sqrt{2}$. A square is inscribed in the circle whose sides are parallel to the $X$ an $Y$ axes. The coordinates of on...
User Avatar
0 votes
0 votes
1 answer
2
Arjun asked Sep 23, 2019
381 views
ISI2014-DCG-55
If $a,b,c$ are sides of a triangle $ABC$ such that $x^2-2(a+b+c)x+3 \lambda (ab+bc+ca)=0$ has real roots then $\lambda < \frac{4}{3}$ $\lambda > \frac{5}{3}$ $\lambda \in \big( \frac{4}{3}, \frac{5}{3}\big)$ $\lambda \in \big( \frac{1}{3}, \frac{5}{3}\big)$
If $a,b,c$ are sides of a triangle $ABC$ such that $x^2-2(a+b+c)x+3 \lambda (ab+bc+ca)=0$ has real roots then$\lambda < \frac{4}{3}$$\lambda \frac{5}{3}$$\lambda \in \bi...
User Avatar
1 votes
1 votes
1 answer
3
Arjun asked Sep 23, 2019
434 views
ISI2014-DCG-56
Two opposite vertices of a rectangle are $(1,3)$ and $(5,1)$ while the other two vertices lie on the straight line $y=2x+c$. Then the value of $c$ is $4$ $3$ $-4$ $-3$
Two opposite vertices of a rectangle are $(1,3)$ and $(5,1)$ while the other two vertices lie on the straight line $y=2x+c$. Then the value of $c$ is$4$$3$$-4$$-3$
User Avatar
1 votes
1 votes
1 answer
4
Arjun asked Sep 23, 2019
362 views
ISI2014-DCG-14
$x^4-3x^2+2x^2y^2-3y^2+y^4+2=0$ represents A pair of circles having the same radius A circle and an ellipse A pair of circles having different radii none of the above
$x^4-3x^2+2x^2y^2-3y^2+y^4+2=0$ representsA pair of circles having the same radiusA circle and an ellipseA pair of circles having different radiinone of the above
User Avatar
Link Copied!