List of top Mathematics Questions on Coordinate Geometry

The equation of the ellipse with foci at ($\pm$3, 0) and the eccentricity as 1/3 is:

The length of the latus rectum and eccentricity of the Hyperbola $9x^{2} - 16y^{2} = 144$ are}

The line $y = mx + 2$ is a tangent to the parabola $y^{2} = 8x$ if}

If the parabola $y^{2} = 4ax$ passes through the point (3, 2) then the length of its latus rectum is:}

The equation of a circle whose Centre is (2, -1) and which passes through the point (3, 6) is

The equation of a circle whose Centre is $(-3, 2)$ and area is $176$ units is:

Let \(P(3\cos\alpha, 2\sin\alpha), \alpha \neq 0\), be a point on the ellipse \(\frac{x^2}{9} + \frac{y^2}{4} = 1\). \(Q\) be a point on the circle \(x^2 + y^2 - 14x - 14y + 82 = 0\) and \(R\) be a point on the line \(x + y = 5\) such that the centroid of the triangle \(PQR\) is \(\left( 2 + \cos\alpha, 3 + \frac{2}{3}\sin\alpha \right)\). Then the sum of the ordinates of all possible points \(R\) is:

Let the vertex A of a triangle ABC be (1, 2), and the mid-point of the side AB be (5, -1). If the centroid of this triangle is (3, 4) and its circumcenter is \((\alpha, \beta)\), then \(2(10\alpha + \beta)\) is equal to:

When the origin is shifted to $(2, 3)$ by translation of axes, the coordinates of a point $P$ become $(1, -2)$. The original coordinates of $P$ are:

If the angle between the pair of lines $x^2 - 2cxy - 7y^2 = 0$ is $\frac{\pi}{3}$, then the value of $c^2$ is:

Let $A(1,0)$, $B(2,-1)$ and $C\left(\dfrac{7}{3},\dfrac{4}{3}\right)$ be three points. If the equation of the bisector of the angle $ABC$ is $\alpha x+\beta y=5$, then the value of $\alpha^2+\beta^2$ is

P is a point on \[ \frac{x^2}{9}+\frac{y^2}{4}=1 \] as \(P(3\cos\alpha,2\sin\alpha)\). Q is a point on \[ x^2+y^2-14x+14y+82=0 \] R is a point on line \[ x+y=5 \] If the centroid of triangle \(PQR\) is \[ \left(\cos\alpha+2,\;\frac{2\sin\alpha}{3}+3\right) \] find the sum of possible ordinates of \(R\).

If \(\left(2\alpha+1,\;\alpha^2-3\alpha,\;\frac{\alpha-1}{2}\right)\) is the image of \((\alpha,2\alpha,1)\) in the line \[ \frac{x-2}{3}=\frac{y-1}{2}=\frac{z}{1}, \] then the value of \(\alpha\) is:

From point \(B(4,8)\) on the parabola \(y^2 = 16x\), two perpendicular chords \(BA\) and \(BC\) are drawn. Given that the locus of the centroid of triangle \(BAC\) is another parabola with length of the latus rectum equal to \(\ell\), then \(3\ell\) is equal to

The area (in square units) of the region \( \{(x, y) : x^2 - 8x \le y \le -x \} \), is

Let \(f(x+y) = f(x) f(y)\), \(f(0) \neq 0\). If \(x^2 g(x) = \int_0^x (t^2 f(t) + t g(t)) \, dt\), then \(g(2)\) is equal to

A bag contains 6 Red and 6 black balls. 6 pair of balls are selected one by one without replacement then the probability that each of the 6 pairs contains 1 red and 1 black ball.

If distance of point (a, 2, 5) from image of point (1, 2, 7) in the line \( \frac{x}{1} = \frac{y-1}{1} = \frac{z-2}{2} \) is 4, then sum of all possible values of a is:

Let foci of a hyperbola be (3, 5) and (3, -4). If eccentricity ‘e’ of the hyperbola satisfies the equation \( 3e^2 - 11e + 6 = 0 \), then the length of the latus rectum of the hyperbola is:

A line \( L : x + y = 0 \) is given. Two lines \( L_1 \) & \( L_2 \) are passing through (-1, -1) inclined at an angle of 45° from line L. Reflection of lines \( L_1 \) and \( L_2 \) in line \( 2y + x = 1 \) is \( ax + by = 9 \) and \( cx + dy = 1 \) then the value of \( |ad + bc| \) is equal to:

Consider a parabola \( y^2 = 8x \). The directrix of parabola cuts x-axis at A and PQ is a focal chord of parabola. If slope of PA = 3/5 and abscissa of P is greater than 1, then the area of \(\Delta AQP\) is:

If \(\left(2\alpha+1,\;\alpha^2-3\alpha,\;\frac{\alpha-1}{2}\right)\) is the image of \((\alpha,2\alpha,1)\) in the line \[ \frac{x-2}{3}=\frac{y-1}{2}=\frac{z}{1}, \] then the value of \(\alpha\) is:

P is a point on \[ \frac{x^2}{9}+\frac{y^2}{4}=1 \] as \(P(3\cos\alpha,2\sin\alpha)\). Q is a point on \[ x^2+y^2-14x+14y+82=0 \] R is a point on line \[ x+y=5 \] If the centroid of triangle \(PQR\) is \[ \left(\cos\alpha+2,\;\frac{2\sin\alpha}{3}+3\right) \] find the sum of possible ordinates of \(R\).

If \( 3\sin t - 12\cos t - 3 = p \), then the sum of all integral values of 'p' such that the equation has at least one real root, is:

Let \( p(x, y) \) be a variable point on the circle \( x^2 + y^2 - 6x - 8y + 21 = 0 \). Then the maximum possible distance from the vertex of \( y^2 + 6y + x + 13 = 0 \) is: