List of top Mathematics Questions on Coordinate Geometry asked in AP EAMCET

The area (in square units) of the triangle formed by the lines 6x² + 13xy + 6y² = 0 and x + 2y + 3 = 0 is:

If the distance between the planes $ 2x + y + z + 1 = 0 $ and $ 2x + y + z + \alpha = 0 $ is 3 units, then the product of all possible values of $ \alpha $ is:

Point (-1, 2) is changed to (a, b) when the origin is shifted to the point (2, -1) by translation of axes. Point (a, b) is changed to (c, d) when the axes are rotated through an angle of 45$^{\circ}$ about the new origin. (c, d) is changed to (e, f) when (c, d) is reflected through y = x. Then (e, f) = ?

The locus of the midpoint of the portion of the line $ x \cos \alpha + y \sin \alpha = p $ intercepted by the coordinate axes, where $ p $ is a constant, is:

Angle between the circles $ x^2 + y^2 - 4x - 6y - 3 = 0 $ and $ x^2 + y^2 + 8x - 4y + 11 = 0 $ is:

The line $ 21x + 5y = k $ touches the hyperbola $ 7x^2 - 5y^2 = 232 $, then $ k $ is:

If $ A = (1,2,3), B = (3,4,7) $ and $ C = (-3,-2,-5) $ are three points then the ratio in which the point C divides AB externally is

The equation $ 2x^2 - 3xy - 2y^2 = 0 $ represents two lines $ L_1 $ and $ L_2 $. The equation $ 2x^2 - 3xy - 2y^2 - x + 7y - 3 = 0 $ represents another two lines $ L_3 $ and $ L_4 $. Let $ A $ be the point of intersection of lines $ L_1 $ and $ L_3 $, and $ B $ be the point of intersection of lines $ L_2 $ and $ L_4 $. The area of the triangle formed by the lines $ AB $, $ L_3 $, and $ L_4 $ is: .

If the lines $ 3x+y-4=0 $, $ x - \alpha y + 10 = 0 $, $ \beta x + 2y + 4 = 0 $ and $ 3x + y + k = 0 $ represent the sides of a square, then find $ \alpha \beta (k+4)^2 $.

If $ \theta $ is the angle between the tangents drawn from the point $ (2,3) $ to the circle $ x^2 + y^2 - 6x + 4y + 12 = 0 $, then $ \theta $ is:

Consider the point $ P(\alpha, \beta) $ on the line $ 2x + y = 1 $. If the points $ P $ and $ (3,2) $ are conjugate points with respect to the circle $ x^2 + y^2 = 4 $, then find $ \alpha + \beta $:

If the circle S = 0 cuts the circles x² + y² - 2x + 6y = 0, x² + y² - 4x - 2y + 6 = 0, and x² + y² - 12x + 2y + 3 = 0 orthogonally, then the equation of the tangent at (0, 3) on S = 0 is:

If $ (a, b) $ and $ (c, d) $ are the internal and external centres of similitude of the circles \[ x^2 + y^2 + 4x - 5 = 0 \] and \[ x^2 + y^2 - 6y + 8 = 0 \] respectively, then $ (a + d)(b + c) $ is:

If the slope of one of the lines in the pair of lines $ 8x^2 + axy + y^2 = 0 $ is thrice the slope of the second line, then $ a = $ ?

Equation of the line touching both parabolas $ y^2 = 4x $ and $ x^2 = -32y $ is:

The area of the triangle formed by the pair of lines $ 23x^2 - 48xy + 3y^2 = 0 $ with the line $ 2x + 3y + 5 = 0 $ is:

If the area of the circum-circle of the triangle formed by the line 2x + 5y + a = 0 and the positive coordinate axes is $\frac{29\pi}{4}$ sq. units, then |a| =

Parametric equations of the circle $ 2x^2 + 2y^2 = 9 $ are:

The orthocentre of the triangle formed by lines $ x + y + 1 = 0 $, $ x - y - 1 = 0 $ and $ 3x + 4y + 5 = 0 $ is:

If $ (1,3) $ is the midpoint of a chord of the circle $ x^2 + y^2 - 4x - 8y + 16 = 0 $, then the area of the triangle formed by that chord with the coordinate axes is:

A line $ L $ passes through $ (1,2,-3) $ and $ (3,3,-1) $, and a plane $ \pi $ passes through $ (2,1,-2), (-2,-3,6), (0,2,-1) $. If $ \theta $ is the angle between $ L $ and $ \pi $, then $ 27 \cos^2 \theta = $ ?

A Circle S passes through the points of intersection of the circles $ x^2 + y^2 - 2x + 2y - 2 = 0 $ and $ x^2 + y^2 + 2x - 2y + 1 = 0 $. If the centre of this circle S lies on the line $ x - y + 6 = 0 $, then the radius of the circle S is:

If the circles $ S = x^2 + y^2 - 14x + 6y + 33 = 0 $ and $ S' = x^2 + y^2 - a^2 = 0 $ (where $ a \in \mathbb{N} $) have 4 common tangents, then the possible number of values of $ a $ is:

A line $ L $ passing through the point $ P(-5,-4) $ cuts the lines $ x - y - 5 = 0 $ and $ x + 3y + 2 = 0 $ respectively at $ Q $ and $ R $ such that \[ \frac{18}{PQ} + \frac{15}{PR} = 2, \] then the slope of the line $ L $ is:

The point (a, b) is the foot of the perpendicular drawn from the point (3, 1) to the line x + 3y + 4 = 0. If (p, q) is the image of (a, b) with respect to the line 3x - 4y + 11 = 0, then $\frac{p}{a} + \frac{q}{b} = $