# Unit 04: Introduction to Analytic Geometry

Here is the list of important questions.

- Find the area between $x-axis$ and the curve $y=4x-x^2$ —
*BSIC Gujranwala (2016)* - Find $h$ if $A(-1,h)$, $B(3,2)$, $C(7,3)$ are collinear —
*BSIC Gujranwala (2016)* - Find the point three fifth of the way along the line segment from $A(-5,8)$, to $B(5,3)$ —
*BSIC Gujranwala (2016)* - Find equation of straight line if its slop is $2$ and $y-intercept$ is $5$. —
*BSIC Gujranwala (2016)* - Transform $5x-12y+39=0$ in two intercept form. —
*BSIC Gujranwala (2016)* - Find angle between the line represented by $2x^2+3xy-5y^2=0$. —
*BSIC Gujranwala (2016)* - Find an equation of the line through the intersection of the lines $x-y-4=0$ and $7x+y+20=0$ and parallel to the line $6x+y-14=0$ —
*BSIC Gujranwala (2016)* - Transform the equation $5x-12y+39=0$ into slope-intercept form. —
*BSIC Gujranwala (2015)* - Find the slope and angle of inclination of the line joining the points $(4,6)$ and $(4,8)$ —
*BSIC Gujranwala (2015)* - Find the point of intersection of the line $x-2y+1=0$ and $2x-y+2=0$. —
*BSIC Gujranwala (2015)* - Find the interior angles of the triangle whose vertices are $A(2,-5)$, $B(-4,-3)$, $C(-1,5)$. —
*BSIC Gujranwala (2015)* - Find the equation of the line represented by $20x^2+17xy-24y^2=0$ —
*BSIC Gujranwala (2015)* - Find the equation of line through the intersection of two lines $x+2y+3=0$ and $3x+4y+7=0$ and making equal intercepts on the axes. —
*BSIC Gujranwala (2015)* - Find the equations of tangents to the circle $x^2+y^2=2$ parallel to the line $x-2y+1=0$ —
*BSIC Gujranwala (2015)* - A quadrilateral has a points $A(9,3)$, $B(-7,7)$, $C(-3,-7)$ and $D(5,-5)$as its vertices. Find the midpoints of its sides. Show that the figure formed by joining the mid-points consecutively is a parallelogram.—
*FBSIC (2017)* - Find equation of two parallel lines perpendicular to $2x-y+3=0$ such that the product of the $x$ and $y-intercepts$ of each is $3$. —
*FBSIC (2017)* - Show that the lines $4x-3y-8=0$, $3x-4y-6=0$ and $x-y-2=0$ are concurrent and the third-line bisects the angle formed by the first two lines. —
*FBSIC (2017)* - Show that points $A(3,1)$, $B(-2,-3)$, $C(2,2)$ are vertices of an isosceles triangle. —
*FBSIC (2016)* - Find an equation of the line through $(-4,-6)$ and perpendicular to the line having slope $-\frac{3}{2}$. —
*FBSIC (2016)* - Prove that the line segment joining the mid-points of two sides of a triangle is parallel to the third side and half as long.—
*FBSIC (2016)* - Find area of triangle determined by points $P$, $Q$ and $R$, $P(0,0,0)$, $Q(2,3,2)$, $R(-1,1,4)$.—
*FBSIC (2016)* - Find the interior angles of the triangle whose vertices are $A(-2,11)$, $B(-6,-3)$, $C(4,-9)$. —
*FBSIC (2016)* - Find co-ordinates of the point that divides the join of $A(-6,3)$ and $B(5,2)$ in the rario $2:3$ —
*BSIC Rawalpandi (2017)* - Find the slope and inclination of the line joining the points $(4,6)$ and $(4,8)$.—
*BSIC Rawalpandi (2017)* - Convert $2x-4y+11=0$ in normal form.—
*BSIC Rawalpandi (2017)* - Find the equation of the line through the point $(2,-9)$ and intersection of the lines $2x+5y-8=0$, $3x-4y-6=0$ —
*BSIC Rawalpandi (2017)* - Find whether the poin $(5,8)$ lies above or below the line $2x-3y+6=0$. —
*BSIC Rawalpandi (2017)* - Find equations of two parallel lines perpendicular to $2x-y+3=0$ such that the product of the $x$ and $y-intercepts$ of each is $3$.—
*BSIC Rawalpindi(2017)* - Transform the equation $5x-12y+39=0$ into intercept form. —
*BSIC Sargodha(2016)* - By means of slope, show that the points $(a,2b)$, $(c,a+b)$, $(2c+a,2a)$ are col-linear. —
*BSIC Sargodha(2016)* - Check whether the given point lies above or below the given line, $P(-7,6);4x+3y-9=0$—
*BSIC Sargodha(2016)* - Find the angle from the line with slope $-\frac{7}{3}$ to the line with slope $\frac{5}{2}$ —
*BSIC Sargodha(2016)* - Find $h$ such that the points $A(h,1)$, $B(2,7)$ and $C(-6,-7)$ are the vertices of a right triangle with right angleat a vertex $A$.—
*BSIC Sargodha(2016)* - Find the point three-fifth of the way along the line segment from $A(-5,8)$ to $B(5,3)$—
*BSIC Sargodha(2017)* - By mean of slope, show that the points $(4,-5)$, $(7,5)$, $(10,15)$ are collinear.—
*BSIC Sargodha(2017)* - Find an equation of line through $A(-6,5)$ having slope $7$.—
*BSIC Sargodha(2017)* - Find an equation of line through $(5,-8)$ and perpendicular to the line with slope $\frac{3}{5}$.—
*BSIC Sargodha(2017)* - Find the distance from the point $(6,-1)$ to the line $6x-4y+9=0$.—
*BSIC Sargodha(2017)* - Find the centre and radius of the circle with equation $4x^2+4y^2-8x-12y-25=0$.—
*BSIC Sargodha(2017)*