# Unit 06: Conic section

Here is the list of important questions.

- Find the centre and radius of the circle given by the equation $4x^2+4y^2-8x+12y-25=0$ —
*BSIC Gujranwala (2016)* - Find equation of tangent to the circle $x^2+y^2=2$ parallel to the line $x-2y+1=0$ —
*BSIC Gujranwala (2016)* - Find focus and directrix of parabola $x^2=-16y$ —
*BSIC Gujranwala (2016)* - Find equation of ellipse with vertices $(0,\pm5)$, eccentricity $\frac{3}{5}$ —
*BSIC Gujranwala (2016)* - Prove vectoprically that in any triangle $ABC$, $a^2=b^2+c^2-2bc \cos A$ —
*BSIC Gujranwala (2016)* - Find equation of circle passing through $A(4,5)$, $B(-4,-3)$, $C(8,-3)$ —
*BSIC Gujranwala (2016)* - Show that the equation $9x^2-18x+4y^2+8y-23=0$ represent an ellipse. —
*BSIC Gujranwala (2016)* - Find the centre and radius of the circle $x^2+y^2-6x+4y+13=0$. —
*BSIC Gujranwala (2015)* - Write the equations of tangent and normal to the circle $x^2+y^2=25$ at $(4,3)$. —
*BSIC Gujranwala (2015)* - Write the equation of parabola with focus $(-3,1)$ and directrix $x=3$. —
*BSIC Gujranwala (2015)* - Find the equation of hyperbola with centre $(0,0)$, focus $(6,0)$ and vertex $(4,0)$. —
*BSIC Gujranwala (2015)* - Prove that the line segment joining the mid-points of two sides of a triangle is parallel to third side and half as long. —
*BSIC Gujranwala (2015)* - Find focus, vertex and directrix of parabola $x^2-4x-8y+4=0$ —
*BSIC Gujranwala (2015)* - Find the equations of two tangents drawn from $(2,3)$ to the circle $x^2+y^2=9$.—
*FBSIC (2017)* - Find the foci, eccentricity and vertices of an ellipse $\frac{(2x-1)^2}{16}+\frac{(y+2)^2}{16}=1$ —
*FBSIC (2017)* - Find the equations of tangents to the conic $9x^2-4y^2=36$ and parallel to the $5x-2y+7=0$ —
*FBSIC (2017)* - Prove that the altitudes of a triangle are constant. —
*FBSIC (2017)* - Find the equation of the circle whose ends of diameter at $(-3,2)$ and $(5,-6)$..—
*FBSIC (2016)* - Find an equation of the parabola whose focus is $F(-3,4)$ and directrix is $3x-4y+5=0$. .—
*FBSIC (2016)* - Find the point of intersection of the given conic $3x^2-4y^2$ and $3y^2-2x^4=7$. .—
*FBSIC (2016)* - Let $\alpha$ be a positive number and $0<c<a$. Let $F(c,0)$ and $F`(-c,0)$ be two given points. Prove that the locus of points $P(x,y)$ such that $|PF|+|PF`|=2a$ is an ellipse. —
*FBSIC (2016 )* - Find the centre and radius of the circle $5x^2+5y^2+14x+12y-10=0$.—
*BSIC Rawalpandi(2017 )* - Determine whether the point $P(-5,6)$ lies outside on or inside the circle $x^2+y^2+4x-6y-12=0$—
*BSIC Rawalpandi(2017 )* - Find focus and vertex of parabola $y^2=-8(x-3)$. —
*BSIC Rawalpandi(2017 )* - Find the foci and eccentricity of an ellipse $25x^2+9y^2=225$.—
*BSIC Rawalpandi(2017 )* - Show that the lines $3x-2y=0$ and $2x+3y-13=0$ are tangent to the circle $x^2+y^2+6x-4yy=0$.—
*BSIC Rawalpandi(2017 )* - Find centre, foci and vertices of the hyperbola $\frac{(x-1)^2}{2}-\frac{(y-1)^2}{9}=1$ —
*BSIC Rawalpandi(2017 )* - Find the equation of the line represented by $20x^2+17xy-24y^2=0$ —
*BSIC Sargodha(2016)* - Find the centre and radius of the circle $4x^2+4y^2-8x+12y-25=0$—
*BSIC Sargodha(2016)* - Find the length of the tangent from the point $P(-5,10)$ to the circle $5x^2+5y^2+14x+12y-10=0$—
*BSIC Sargodha(2016)* - Find the coordinates of foci and vertices of ellipse $25x^2+9y^2=225$—
*BSIC Sargodha(2016)* - Find the foci and eccentricity of the hyperbola $\frac{y^2}{16}-\frac{x^2}{49}=1$ —
*BSIC Sargodha(2016)* - Find the coordinates of the points of intersection of the line $x+2y=6$ with the circle $x^2+y^2-2x-2y-39=0$—
*BSIC Sargodha(2016)* - Prove that in any triangle $ABC$, $b^2=c^2+a^2-2ca \cos B$–
*BSIC Sargodha(2016)* - Find focus and vertex of $x^2=-16y$.—
*BSIC Sargodha(2017)* - Find eccentricity of ellipse $\frac{x^2}{2}+\frac{y^2}{18}=1$.—
*BSIC Sargodha(2017)* - Define vertices and co-vertices of an ellipse.—
*BSIC Sargodha(2017)* - Find focus, vertex and directrix of $x+8-y^2+2y=0$ .—
*BSIC Sargodha(2017)* - Find the points of intersection of the conic $y=1+x^2$ and $y=1+4x-x^2$.—
*BSIC Sargodha(2017)*