# 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)