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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.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.Three identical cones each have a radius of 50 and a height of 120. The cones are placed so that their circular bases are touching each other. A sphere is placed so that it rests in the space created by the three cones, as shown. If the top of the sphere is level with the tops of the cones, then the radius of the sphere is closest to

(A) 38.9 (B) 38.7 (C) 38.1 (D) 38.5 (E) 38.3

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.

find locus of circumcenter of triangle PTQ is

ans y square =x-2

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

^{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 circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4 and x + 2y = 5

x+ 4y= 12, is(A) 1 (B) 2 (C) 12 (D) $\frac{9}{2}$

^{2}/ 4 ) + ( y^{2}/9 ) .find 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}+2y^{2}=1 subtends a right angle at the centre of the ellipse isFind 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.

^{2}+2y -3x +5 =0.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

find the vertex, focus, diretrix and length of latus-rectum of the parabola

^{2}- 4y - 2x - 8 = 0^{2}+ 3y - 4x -3 = 0^{2}- 16x - 12y - 57 = 0The 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

passed through the focus F1 and F2 of the ellipse. Two curves intersect at

four points. Let P be any point of intersection. If the major axis of the

ellipse is 15 and the area of the triangle PF1F2 = 26 , then find the value of

4a^2 - 4b^2.

find the equation of the circle passing through origin and cutting off intercepts a and b from x axis and y axis

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.

^{2}-y^{2}=a^{2}is h^{2.}Find the standard equation of ellipse whose focus is (1,0), the directrix is x+y+1=0 and eccentricity is 1/root2

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) isA 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}=6^{2}=32x ; then the other end of the chord isif 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

$\left|\begin{array}{ccc}{x}_{1}& {y}_{1}& {x}_{1}{y}_{1}\\ {x}_{2}& {y}_{2}& {x}_{2}{y}_{2}\\ {x}_{3}& {y}_{3}& {x}_{3}{y}_{3}\end{array}\right|=0$

the 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

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

Find 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)

Q.41. Let P be a point on the circle ${x}^{2}+{y}^{2}=9$, Q a point on the line 7x + y + 3 = 0, and the perpendicular bisector of PQ be the line x - y + 1 = 0. Then, the coordinates of P are

(a) (3, 0)

(b) (0, 3)

(c) (72 / 25, - 21 / 25)

(d) (- 72 / 25, - 21 / 25)

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

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

the equation of the tangent at the point (0,0) to the circle , making intercepts of length 2a and 2b units on the coordinate axes areans is ax+ by = 0 and ax - by = 0Please 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 .

_{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 }= -1A 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.

In case of parabola

y= x

^{2}-2x-3Find:

a)Vertex:

b)Axis:

c)Focus:

d)Directrix:

e)Latus Rectum:

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 iswhat will be the point of contact of the given circles : x

^{2}+y^{2}-6x -6y +10 =0 and x^{2}+y^{2}=2find the equation of ellipse .the distance between foci is 8 unit and the distance between directrix is 18 units.

^{2}+y^{2}=a^{2}meets the tangent at a fixed point A (a,0) in T and T is joined to B, the other end of diameter through A. Prove that the locus of intersection of AP and BT is an ellipse whose 'e' is 1/root2find 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

anda_{1}x+b_{1}y+c_{1}=0cut the coordinate axis at concyclic points ,then prove thata_{2}x+b_{2}y+c_{2}=0.a_{1}a_{2}=b_{1}b_{2}what is co-axial circle how to determine its equation and also tell its figure

find the focus and equation of parabola whose vertex is (6,-3) and diretrix is 3x - 5y + 1 = 0.

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

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) .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.

If P is any point on hyperbola whose axis are equal,prove that SP.S'P=CP

^{2 }?^{2}/a^{2 }+y^{2}/b^{2}is b^{2}Find the equation of the circle with radius 5 whose centre lies on x-axis & passes through the point (2,3)?

Show that the 4 points (0,0),(1,1),(5,-5) and (6,-4) are concyclic.Please answer it fast , very urgent!!!!!!