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Syllabus

Find the equation of the common tangent of parabola y

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

^{2}= 4ax is a harmonic mean between the segment of any focal chord.^{2}+2y -3x +5 =0.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

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

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

^{2}+y^{2 }=36, whereas the point (6,8) is outside the circlefind the locus of the mid point of the portion of the line x cosa +yp sin a = p which is intercepted between the axis ??

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 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

1)touches y axis at (0,?3) and passes through (-1,0)

2)touches the line 2x-3y-7=0 at (2,-1) and passes through (4,1)

3)touches the line 3x+y+3=0 at (-3,6) and tangent x+3y-7=0.

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

^{2}+y^{2}-6x+4y-36=0 represents a circle.Also find its centre and radius.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}is tangent to the hyperbola x^{2}/a^{2}- y^{2}/b^{2}= -1. Find the locus of the middle point of PQ.^{2}/ 4 ) + ( y^{2}/9 ) .Find the standard equation of ellipse whose focus is (1,0), the directrix is x+y+1=0 and eccentricity is 1/root2

find the equation of the circle concentric with the circles x^2 + y^2 -4x +6y-3=0 and of double its (1) circumference (2) area

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

Prove that

PM^2 = Latus rectum × PN ?

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

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

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)

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.

Q10. Find the centre and the radius of the circle x

^{2}^{ }+ y^{2}– 4x + 2y – 4 = 0. Hence or otherwise, prove that x + 1 = 0 is a tangent to the circle. Calculate the coordinates of the point of contact. If this point of contact is A, find the coordinates of the other end of the diameter through A.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.find the focus and equation of parabola whose vertex is (6,-3) and diretrix is 3x - 5y + 1 = 0.

how can we derive standard equation of ellipse

Find the equation of parabola :

vertex =(2,1)

directrix : x = y-1

given directrix is 3x-5y+1=0 & vertex is (-6,0),find focus and eqn of parabola

(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

Find the equation of the hyperbola having its foci at (0,root14) and (0,-root14) and passing through the point P(3,4)...

In case of parabola

y= x

^{2}-2x-3Find:

a)Vertex:

b)Axis:

c)Focus:

d)Directrix:

e)Latus Rectum:

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 .

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}+y^{2}+z^{2}+2ux+2vy+2wz = 0If 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 isfind locus of circumcenter of triangle PTQ is

ans y square =x-2

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) is^{2}+2y^{2}=1 subtends a right angle at the centre of the ellipse isfind 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

find the equation of ellipse .the distance between foci is 8 unit and the distance between directrix is 18 units.

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

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) .1)

if parabola y^{2}=px passes through point (2,-3),find the length of latus rectum .2) find the value of p so that the equation x^{2}+y^{2}- 2px+ 4y - 12=0 may represent a circle of radius 5 units .3) one end of the diameter of a circle x2+y2-6x+5y-7=0 os (7,-8).find the co-ordinates of other end

â€‹QA- 5. Which one of the following equations parametrically represents equation to a parabolic profile?

(A) x = 3 cos t ; y = 4 sin t (B) â€‹â€‹ x

^{2}–2 = – 2 cos t ; y = 4 cos^{2}$\frac{t}{2}$(C) $\sqrt{\mathrm{x}}=\mathrm{tan}\mathrm{t};\sqrt{\mathrm{y}}=\mathrm{sec}\mathrm{t}$ (D) x = $\sqrt{1-\mathrm{sint}};\mathrm{y}=\mathrm{sin}\frac{\mathrm{t}}{2}+\mathrm{cos}\frac{\mathrm{t}}{2}$

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.

Find the equation of circle passing through the origin,radius 17 and ordinate of the centre is -15.

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

^{2 }?^{2}+36y^{}^{2}-4x+24y+1=0 at the point(1/2,-2/3)Find the equations of the tangents and normals to the ellipse

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

Q.17. The radius of the circle whose two normals are represented by the equation ${x}^{2}-5xy-5x+25y=0$ and which touches externally the circle ${x}^{2}+{y}^{2}-2x+4y-4=0$ will be-

(A) 21

(B) 2

(C) 3

(D) 14

^{2}+y^{2}+6x+4y-5=0 and x^{2}+y^{2}-6x-8y+1=0 and whose radius is 3.2.Find the equation of the circle which passes through the points intersection of x

^{2}+y^{2}-4=0 and x^{2}+y^{2}-2x-4y+4=0 and touches the line x+=0.