A circle C1 passes through the origin O and has diameter 4 on the positive x-axis. The line y = 2x gives a chord OA of circle C1. Let C2 be the circle with OA as a diameter. If the tangent to C2 at the point A meets the x-axis at P and y-axis at Q, then QA :AP is equal to
A circle C1 passes through the origin O and has diameter 4 on the positive x-axis. The line y = 2x gives a chord OA of circle C1. Let C2 be the circle with OA as a diameter. If the tangent to C2 at the point A meets the x-axis at P and y-axis at Q, then QA :AP is equal to
- 1 : 4
- 1 : 5
- 2 : 5
- 1 : 3
The Correct Option is A
Solution and Explanation
The correct answer is (A) : 1 : 4
Equation of C1
x2 + y2 – 4x = 0
Intersection with
y = 2x
\(x^2+4x^2-4x = 0\)
\(5x^2-4x = 0\)
\(⇒ x = 0, \frac{4}{5}\)
\(y = 0, \frac{8}{5}\)
\(A : (\frac{4}{5}, \frac{8}{5})\)
Tangent of \(C_2\) at \(A(\frac{4}{5},\frac{8}{5})\)
x+2y = 4
\(⇒ P : (4,0), Q : (0,2)\)
\(QA : AP = 1:4\)
Top JEE Main Mathematics Questions
- Let $S = \{\theta \in (-2\pi, 2\pi) : \cos\theta + 1 = \sqrt{3} \sin\theta\}$. Then $\sum_{\theta \in S} \theta$ is equal to:
- JEE Main - 2026
- Mathematics
- Trigonometry
If for \( 3 \leq r \leq 30 \), \[ \binom{30}{30-r} + 3\binom{30}{31-r} + 3\binom{30}{32-r} + \binom{30}{33-r} = \binom{m}{r}, \] then \( m \) equals: ________
- JEE Main - 2026
- Mathematics
- Combinatorics
- The number of points in the interval \( [2, 4] \), at which the function \( f(x) = \left\lfloor x^2 - x - \frac{1}{2} \right\rfloor \), where \( \left\lfloor \cdot \right\rfloor \) denotes the greatest integer function, is discontinuous, is _______.
Let \[ \alpha = \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \dots \infty \] and \[ \beta = \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \dots \infty. \]
Then the value of \[ (0.2)^{\log_{\sqrt{5}}(\alpha)} + (0.04)^{\log_{5}(\beta)} \] is equal to: ________- JEE Main - 2026
- Mathematics
- Sequences and Series
Let \( y = y(x) \) be the solution of the differential equation:
\[ \frac{dy}{dx} + \left( \frac{6x^2 + (3x^2 + 2x^3 + 4)e^{-2x}}{(x^3 + 2)(2 + e^{-2x})} \right)y = 2 + e^{-2x}, \quad x \in (-1, 2) \]
satisfying \( y(0) = \frac{3}{2} \).
If \( y(1) = \alpha \left(2 + e^{-2}\right) \), then the value of \( \alpha \) is ________.- JEE Main - 2026
- Mathematics
- Differential Equations
Top JEE Main Circle Questions
- If the circles \( (x+1)^2 + (y+2)^2 = r^2 \) and \( x^2 + y^2 - 4x - 4y + 4 = 0 \) intersect at exactly two distinct points, then
- If one of the diameters of the circle \(x^2+y^2-10x+4y+13=0\) is a chord of another circle and whose center is the point of intersection of the lines \(2x + 3y = 12\) and \(3x - 2y = 5 \) then the radius of the circle is
Four distinct points \( (2k, 3k), (1, 0), (0, 1) \) and \( (0, 0) \) lie on a circle for \( k \) equal to:
- If the center and radius of the circle $\left|\frac{z-2}{z-3}\right|=2$ are respectively $(\alpha, \beta)$ and $\gamma$, then $3(\alpha+\beta+\gamma)$ is equal to
- Let $y=x+2,4 y=3 x+6$ and $3 y=4 x+1$ be three tangent lines to the circle $(x-h)^2+(y- k )^2= r ^2$ Then $h + k$ is equal to :
Top JEE Main Questions
- 1 mole of ideal diatomic gas is enclosed in a cylinder piston arrangement having cross-sectional area of piston \(4\,\text{cm}^2\). If gas has only rotational modes and \(P_{atm}=100\ \text{kPa}\), some amount of heat is added to the system as a result piston moves up slowly by \(2.5\,\text{cm}\). If temperature change is \(1.2^\circ C\). Find heat given to gas.
- JEE Main - 2026
- Thermal Physics
- Let $S = \{\theta \in (-2\pi, 2\pi) : \cos\theta + 1 = \sqrt{3} \sin\theta\}$. Then $\sum_{\theta \in S} \theta$ is equal to:
- JEE Main - 2026
- Trigonometry
Refer the figure below. \( \mu_1 \) and \( \mu_2 \) are refractive indices of air and lens material respectively. The height of image will be _____ cm.
- JEE Main - 2026
- Optics and Refraction
In single slit diffraction pattern, the wavelength of light used is \(628\) nm and slit width is \(0.2\) mm. The angular width of central maximum is \(\alpha \times 10^{-2}\) degrees. The value of \(\alpha\) is ____.
- JEE Main - 2026
- Interference and Diffraction
\(t_{100\%}\) is the time required for 100% completion of a reaction, while \(t_{1/2}\) is the time required for 50% completion of the reaction. Which of the following correctly represents the relation between \(t_{100\%}\) and \(t_{1/2}\) for zero order and first order reactions respectively
- JEE Main - 2026
- Zero-order Reactions
Concepts Used:
Circle
A circle can be geometrically defined as a combination of all the points which lie at an equal distance from a fixed point called the centre. The concepts of the circle are very important in building a strong foundation in units likes mensuration and coordinate geometry. We use circle formulas in order to calculate the area, diameter, and circumference of a circle. The length between any point on the circle and its centre is its radius.
Any line that passes through the centre of the circle and connects two points of the circle is the diameter of the circle. The radius is half the length of the diameter of the circle. The area of the circle describes the amount of space that is covered by the circle and the circumference is the length of the boundary of the circle.
Also Check: