Coordinate Geometry is an important topic in the Mathematics section in TS EAMCET exam. Practising this topic will increase your score overall and make your conceptual grip on TS EAMCET exam stronger.
This article gives you a full set of TS EAMCET PYQs for Coordinate Geometry with explanations for effective preparation. Practice of TS EAMCET Mathematics PYQs including Coordinate Geometry questions regularly will improve accuracy, speed, and confidence in the TS EAMCET 2026 exam.
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TS EAMCET PYQs for Coordinate Geometry with Solutions
1.
A circle passing through the points \( (1, 1) \) and \( (2, 0) \) touches the line \( 3x - y - 1 = 0 \). If the equation of this circle is \( x^2 + y^2 + 2gx + 2fy + c = 0 \), then a possible value of \( g \) is- \(-\frac{5}{2}\)
- \(-\frac{3}{2}\)
- 6
\(-5\)
2.
The line L: $6x+3y+k=0$ divides the line segment joining the points (3,5) and (4,6) in the ratio -5:4. If the point of intersection of the lines L = 0 and $x-y+1=0$ is P(g,h) then h =- 2g
- 2g-1
- 3g
- g+1
3.
If $\text{Tan}^{-1}(2\sqrt{10})$ is the angle between the lines $ax^2+4xy-2y^2=0$ and $a \in \mathbb{Z}$, then the product of the slopes of given lines is- $\frac{3}{2}$
- $\frac{2}{3}$
- $-\frac{2}{3}$
- $-\frac{3}{2}$
4.
The circles \(x^2 + y^2 + 2x - 6y - 6 = 0\) and \(x^2 + y^2 - 6x - 2y + k = 0\) are two intersecting circles and \(k\) is not an integer. If \( \theta \) is the angle between the two circles and \( \cos \theta = -\frac{5}{24} \), then find \( k \).- \( \frac{6}{5} \)
- \( \frac{74}{9} \)
- \( \frac{37}{3} \)
- \( \frac{53}{7} \) \bigskip
5.
The radius of a circle $C_1$ is thrice the radius of another circle $C_2$ and the centres of $C_1$ and $C_2$ are (1,2) and (3,-2) respectively. If they cut each other orthogonally and the radius of the circle $C_1$ is 3r, then the equation of the circle with r as radius and (1,-2) as centre is- $x^2+y^2-2x+4y-3=0$
- $x^2+y^2-2x+4y+7=0$
- $x^2+y^2-2x+4y-7=0$
- $x^2+y^2-2x+4y+3=0$
6.
A straight line through the point P(1,2) makes an angle $\theta$ with the positive X-axis in anti-clockwise direction and meets the line $x+\sqrt{3}y-2\sqrt{3}=0$ at Q. If $PQ = \frac{1}{2}$, then $\theta=$- $\frac{\pi}{6}$
- $\frac{5\pi}{6}$
- $\frac{2\pi}{3}$
- $\frac{\pi}{3}$
7.
A circle C touches the X-axis and makes an intercept of length 2 units on the Y-axis. If the centre of this circle lies on the line $y=x+1$, then a circle passing through the centre of the circle C is- $x^2+y^2-2x-4y+1=0$
- $x^2+y^2-26x-20y+19=0$
- $x^2+y^2-20x-26y+19=0$
- $x^2+y^2+2x-4y+1=0$
8.
If the direction ratios of two lines are \( (3,0,2) \) and \( (0,2,k) \), and \( \theta \) is the angle between them, and if \( |\cos \theta| = \frac{6}{13} \), then \( k = \)- \( \pm 2 \)
- \( \pm 3 \)
- \( \pm 5 \)
- \( \pm 7 \)
9.
If the centre $(\alpha, \beta)$ of a circle cutting the circles $x^2+y^2-2y-3=0$ and $x^2+y^2+4x+3=0$ orthogonally lies on the line $2x-3y+4=0$, then $2\alpha+\beta=$- 3
- -3
- 0
- 1
10.
A line meets the circle $x^2+y^2-4x-4y-8=0$ in two points A and B. If P(2,-2) is a point on the circle such that PA = PB = 2 then the equation of the line AB is- $2x+3y=0$
- $3x+2y=0$
- $2x+3=0$
- $2y+3=0$
11.
The lines $x-2y+1=0$, $2x-3y-1=0$ and $3x-y+k=0$ are concurrent. The angle between the lines $3x-y+k=0$ and $mx-3y+6=0$ is $45^\circ$. If m is an integer, then $m-k=$- -6
- 18
- 6
- -18
12.
If $m_1, m_2$ are the slopes of the tangents drawn through the point $(-1,-2)$ to the circle $(x-3)^2+(y-4)^2=4$, then $\sqrt{3}|m_1-m_2|=$- 1
- 2
- 3
- 4
13.
If $2x^2+xy-6y^2+k=0$ is the transformed equation of $2x^2+xy-6y^2-13x+9y+15=0$ when the origin is shifted to the point $(a,b)$ by translation of axes, then k =- 1
- 0
- 21
- 15
14.
If the equation of the circumcircle of the triangle formed by the lines $L_1=x+y=0$, $L_2=2x+y-1=0$, $L_3=x-3y+2=0$ is $\lambda_1 L_2 L_3 + \lambda_2 L_3 L_1 + \lambda_3 L_1 L_2 = 0$, then $\frac{7\lambda_1+\lambda_3}{\lambda_2} =$- 1
- 2
- 3
- 4
15.
The pole of the line \(x - 5y - 7 = 0\) with respect to the circle \(S \equiv x^2 + y^2 - 2x - 2y + 1 = 0\) is \(P(a,b)\). If \(C\) is the centre of the circle \(S = 0\) then \(PC =\):- \( \sqrt{a + b - 1} \)
- \( \sqrt{a^2 + b^2 - 1} \)
- \( \sqrt{a^3 + b^3 - 1} \)
- \( 3ab \)
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