List of top Mathematics Questions on Coordinate Geometry asked in KEAM

The equation of a chord to the circle $x^{2}+y^{2}=25$ is $x+y-5=0$. The equation of a circle whose diameter is $x+y-5=0$, is}

The eccentricity of the hyperbola $25x^{2}-36y^{2}-50x-72y-911=0$, is

Let the eccentricity of an ellipse be $\frac{1}{2}$. If $S(3,2)$ is a focus and $x-9=0$ is the corresponding directrix of the ellipse, then the equation of the ellipse is}

The nearest point on the line $x+2y=5$ from the point $P(7,9)$ is equal to

The length of the latus rectum of the ellipse $225x^{2}+125y^{2}=28125$ is}

Let O be the origin and R be any point on $y^{2}=2x$. The locus of the midpoint of the line segment OR, is

A straight line has y -intercept -5. If it makes $120^{\circ}$ with the x-axis, then the equation of the line is

If \( ay = x + b \) is the equation of the line passing through the points (-5, -2) and (4, 7), then the value of \( 2a + b \) is equal to:

If the line \( 2x - 3y + c = 0 \) passes through the focus of the parabola \( x^2 = -8y \), then the value of \( c \) is equal to:

The three vertices of a triangle are \( (0,0), (3,1) \) and \( (1,3) \). If this triangle is inscribed in a circle, then the equation of the circle is:

The angle between the lines $$ \frac{x-1}{2} = \frac{2y+3}{4} = \frac{z+5}{-2} \quad \text{and} \quad \frac{x-3}{4} = \frac{y+1}{-4} = \frac{z+3}{-4} $$ is equal to 

The line joining the points $ (2,2,2) $ and $ (6,6,6) $ meets the line $$ \frac{x - 1}{3} = \frac{y - 2}{2} = \frac{z - 5}{-1} $$ at the point 

The number of solutions of the equation \( \dfrac{1}{2}(x^3+1)=(2x-1)^{⅓}\) is 

Suppose P is the point on the line joining  \((-9,4,5)\) and \((11,0,-1)\) that lies closest to the origin O. Then \(|OP|^2\) equals to?

If (2,-6),(5,2) and (-2,2) constitute the vertices of a triangle then the the line joining the origin and its orthocentre is

The three vertices of a triangle are (0, 0), (3, 1) and (1, 3). If this triangle is inscribed in a circle, then the equation of the circle is

If x+13y=40 is normal to the curve y=5x²+ax+β at the point (1, 3), then the value of αß is equal to

The angle between the planes x=√3 and z = √2 is equal to

If \(\theta\) is angle between the lines \(\frac{x}{1}=\frac{y+1}{2}=\frac{z-1}{3}\) and \(\frac{x+1}{3}=\frac{y}{2}=\frac{z}{1}\), then \(\cos\theta=\)

If the radius of the circle x²+y²+ax+by+3=0 is 2, then the point (a, b) lies on the circle

The points of intersection of the line y=x+2 and the circle (x-2)² + y² = 16 are