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Syllabus

Find the equation of the common tangent of parabola y

^{2}=4ax and x^{2}=4by.Show that the semi latus rectum of the parabola y

^{2}= 4ax is a harmonic mean between the segment of any focal chord.2. Consider the circle x

^{2}+ y^{2}- 8x - 18y + 93 = 0 with cantre 'C' and are point P( 2, 5 ) outside it. From the point P, a pairof tangents PQ and PR are drawn to the circle with S as the midpoint of QR.

The line joining P to C intersects the given circle at A and B Which of the following hold(s) good?

(A) CP is the arithmetic mean of AP and BP.

(B) PR is the geometric mean of PS and PC.

(C) PS us the harmonic mean of PA and PB.

(D) The angle between the two tangents from P is tan

^{-1}$\left(\frac{3}{4}\right).$an equilateral triangle is inscribed in the parabola y

^{2}=4ax,where one vertex is at the vertex of the parabola.find the length of the side of the triangle.pls answer me as soon as possible.The focus of parabola is (1,5) and its directrix is x + y + 2 = 0. Find the equation of the parabola, its vertex and length of latus rectum.

the line lx + my +n=0 is a normal to the parabola y^2 = 4ax if

find the equation of the circle circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4 and x + 2y = 5

if the chord of contact of tangents from a point P(h,k) to the circle x^{2}+ y^{2}= a^{2}touches the circle x^{2}+ (y-a)^{2}= a^{2}, then locus of P isfind the locus of the mid point of the portion of the line x cosa +yp sin a = p which is intercepted between the axis ??

^{2}+ y^{2}= 100 that passes through (1,7) and subtends an angle of 120 at the origin is what?Find the equation of the circle which has its centre at the point (3,4) and touches the straight the line 5x+12y-1=0.

Find the equqtion of the circle which touches the axes and whose centre lies on x-2y=3.

A circle whose centre is the point of the intersection of the lines 2x-3y+4=0 and 3x+4y-5=0 passes through the origin. find its equation.

A circle of radius 4 units touches the coordinate axes in the first quadrant. Find the equation of its images with respect to the line mirrors x=0 and y=0.

One diameter of the circle circumscribing the rectangle ABCD is 4y=x+7. If the coordinates of A and B are (-3,4) and (5,4) respectively. Find its equation.

Find the equations of circle passing through the points (1,1),(2,2) and whose radius is 1 units?

Prove that (-1,6), (5,2), (7,0), and (-1,-4) are concyclic.

e

if y = 2x is a chord of the circle x

^{2}+ y^{2}- 10x =0find the equation of the circle with this chord as diameter

Q Read the following write up carefully and answer the following questions:Q. Let ABC be triangle whose equation of sides are AB $\equiv $ x + 2y = 3, AC $\equiv $2x + y = 3 and BC$\equiv $x + y = 4. S

_{l}, S_{2}, S_{3}are three circles drawn considering AB, AC and BC as diameter respectively. The radical axis of S_{1}and S_{2}, S_{l}and S_{3}and S_{2}and S_{3}are L_{12}= O, L_{13}= O, L_{23}= O. These radical axes meet sides BC, AC and AB at D, E and F respectively and triangle DEF is formed.Q. 1. Equation to circumcircle of triangle ADC is(A) x

^{2}+y^{2}-6x+4=0 (B) x^{2}+y^{2}-6y+4=0(C) x

^{2}+y^{2}+6x+4=0 (D) None of these.The centre of a circle passing through the points (0,0) & (1,0) & touching the circle x2+y2=9 is: ans is (1/2 , +-root2)..explainAB is a chord of circle x2+y2=25 . The tangents of A & B intersect at C. If (2,3) is the mid-point of AB , the area of quadrilateral OACB is:ams is 50root (3/13) plzz explain3. Extremities of a dagonal of a rectangle are (0,0) & (4,3).Find the equations of the tangents to the circumcentre ofthe reactangle which are parallel to this diagonal.4. Find the equ. of circle described on the common cord of the circles x2+y2-4x-5=0 & x2+y2+8y+7=0 as diameter.ans is x2+y2-2x+4y+1=0..explain.The parametric equations of a parabola are x=t

^{2}+1, y=2t+1.The cartesian equation of its directrix isa) x=0 b)x+1=0 c)y=0 d) none of these

In an ellipse, x

^{2}/a^{2}+ y^{2}/b^{2}= 1, a>b, if the focal distances of a point on the ellipse ( the point is neither on X-axis nor on Y-axis ) are r_{1}and r_{2}, then find the length of the normal drawn at this point ( length of normal means the length of the portion of the normal between the point and the major axis ) ?^{2}+3y^{2}=k^{2.}find the equation of the circle passing through origin and cutting off intercepts a and b from x axis and y axis

^{2}/ 4 ) + ( y^{2}/9 ) .one diameter of the circle circumscribing the rectangle ABCD is 4y=x+7.If the coordinates of A & B are (-3,4) &(5,4) respectively , find the equation of the circle.

Find the standard equation of ellipse whose focus is (1,0), the directrix is x+y+1=0 and eccentricity is 1/root2

A circle of constant radius 'a' passes through origin 'O' and cuts the coordinate axes in points P and Q, then the equation of the locus of the foot of perpendicular from O to PQ is

(a) (x^2+y^2)(1/x^2+1/y^2)=4a^2

(b) (x^2+y^2)(1/x^2+1/y^2)=a^2

(c) (x^2+y^2)^2(1/x^2+1/y^2)=4a^2

(d) (x^2+y^2)(1/x^2+1/y^2)=a^2

a tangent to the ellipse x

^{2}+ 4y^{2}=4 meets the ellipse x^{2}+2y^{2}=6 at P and Q.the angle between the tangents at P and Q of the ellipse x^{2}+2y^{2}=6if the line 2x - y +1 = 0 touches the circle at the point (2,5) and the center of the circle lies on the line x+y -9 =0 find the eqn of circle

^{2}= 4x which are closest to the circle x^{2}+ y^{2}- 24y + 128 = 0 area) (4,4)

b)(0,0)

c) (0,2root2)

d) none

^{2}+30x+2y+59=0the tangent to curv y= x^2 + 6 at a point 1,7 touches the circle x^2+y^2+16x+12y+c=0 at a point q then the coordinates of q are :

ans = -6,-7

^{2}+y^{2}+z^{2}+2ux+2vy+2wz = 0Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4

x+y= 16.A tangent to the ellipse 4x2+9y2=36 is cut by the tangent at the extremities of the major axis at T and T'. The circle on TT' as diameter passes through the point

(A) (0-$\sqrt{}$5) (B) ( $\sqrt{}$ 5, 0 )

(C) (0,0) (D) (3,2)

3x-4y+1=0 at (1,1) and having radius 10 unit.

The foci of a hyperbola coincide with the foci of the ellipse x2/25 + y2/9=1.Find the equation of the hyperbola,if its eccentricity is 2.

The equations of the tangents drawn from the origin to the circle x

^{2}+ y^{2}- 2rx- 2hy + h^{2}=0 are :^{2}-r^{2})x-2rhy=0, x=0^{2}-r^{2})x + 2rhy=0,x=0.how can we derive standard equation of ellipse

^{2}+y^{2}-6x+4y-36=0 represents a circle.Also find its centre and radius.Find the equation of parabola :

vertex =(2,1)

directrix : x = y-1

(A) straight line parallel to x-axis (B) straight line parallel to y-axis

(C) circle of radius sq.rt.2 (D) circle of radius sq.rt.3

(1) 1 (2) $\sqrt{2}$ (3) $2\sqrt{2}$ (4) 3

Please do this question both by Maxima and minima and simple method . Please please please do it by both the methods . Do not forget to do it by both the methods .

Calculate the coordinates of the foot of perpendicular from the point (-4,2) to the line 3x + 2y = 5. also find the equation of the smallest circle passing through (-4,2) and having its centre on the line 3x + 2y = 5

A man running a race course notes that the sum of the distances from the two flag posts from him is always 10m and the distance between the flag posts is 8 metres. Find the equation of the path traced by the man.

^{2}+ by^{2}+ cz^{2}= 1.If P(-3,2) is one end of the focal chord PQ of the parabolay^2+4x+4y=0, then the slope of the normal at Q is^{2}/a^{2}+ y^{2}/b^{2}= 1.the angle subtended by common tangents of two ellipses 4(x-4)

^{2 }+25y^{2}=100 4(x+1)^{2}+ y^{2}=4 at the origin (in degrees) isfind the equation of ellipse .the distance between foci is 8 unit and the distance between directrix is 18 units.

find the equation of circle whose centre is the point of intersection of the lines 2x-3y+4=0 and 3x+4y-5=0 passes through the origin.

find the equation of circle which passes through the centre of the circle x

^{2}+y^{2}-4x-8y-41=0 and is concentric with x^{2}+y^{2}-2y+1=0prove tht points (2,-4)(3,-1)(3,-3)(0, 0)are concyclic

answer fast.urgent

what is co-axial circle how to determine its equation and also tell its figure

^{2}-16y^{2}-18x -64y-199=0 represents the equation of a hyperbola ; find the coordinate of its centre & also the equations of its directrices.

Show that the circle on the chord xcosα + ysinα - p = 0 of the circle x

^{2}+y^{2}= a^{2}as diameter is x^{2}+ y^{2}- a^{2}-2p(xcosα +ysinα -p)=0a.)1

b.)4

c.)6

d.)8

^{2}+y^{2}-4x=0 which is bisected at the point (1,1).{Please mention the requires formula in details)

The bisector of two line L1 and L2 are given by 3x^2-8xy-3y^2+10x+20y-25.If the line L1 passes through the origin find L2???

Find the distance between the chords of contact of the tangent to the circle x

^{2 }+y^{2 }+2gx+2fy+c=0 from the origin and the point (g,f) .x+ 4y= 12, is(A) 1 (B) 2 (C) 12 (D) $\frac{9}{2}$

A circle of radius 2 lies in the first quadrant and touches both the axis.Find the equation of the circle with the centre at (6,5) and touching the above circle externally.

_{1}^{2},2at_{1}) , (at_{2}^{2},2at_{2}) on the parabola y^{2}=4ax are at right angles if______{1}t_{2}= -2_{1}t_{2}= 1_{1}t_{2}= 2_{1}t_{2 }= -1If P is any point on hyperbola whose axis are equal,prove that SP.S'P=CP

^{2 }?find the equation of the parabola whose focus is the point (2,3) and dirictrix is the line x-4y+3=0 also find the lenth of its latusrectum

Find the equation of the circle with radius 5 whose centre lies on x-axis & passes through the point (2,3)?

^{2}+2y -3x +5 =0.In case of parabola

y= x

^{2}-2x-3Find:

a)Vertex:

b)Axis:

c)Focus:

d)Directrix:

e)Latus Rectum: