Find the equation of the common tangent of parabola y²=4ax and x²=4by.

Show that the semi latus rectum of the parabola y² = 4ax is a harmonic mean between the segment of any focal chord.

The equation of the hyperbola whose directrix is x+2y=1,focus (2,1) and eccentricity 2 will be?

an equilateral triangle is inscribed in the parabola y²=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.

 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.

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 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.

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

In case of parabola

y= x²-2x-3

Find:

a)Vertex:

b)Axis:

c)Focus:

d)Directrix:

e)Latus Rectum:

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

1. Find the equation of the circles which touch the axis of x at a distance of 4 from the origin and cut off an intercept of 6 from the axis of y
2. A circle having its centre in the first quadrant touches the y axis at a point (0,2) and passes through the point (1,0).Find the equation of the circle 
3. calculate the co ordinatesof the foot of the perpendicular from the point (-4,2)to the line 3x+2y=5 . find the equation of the smallest circle passing through(-4,2) and having its centre on the line 3x+2y=5        

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 ??

 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.

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if y = 2x is a chord of the circle x² + y² - 10x =0

find the equation of the circle with this chord as diameter

an ellipse whose foci are(2,4 and (14,9) and touches x)-axis ,then its eccentricity is ?

1. 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)..explain
2. AB 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 explain

3. 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=t² +1, y=2t+1.The cartesian equation of its directrix is

a) x=0 b)x+1=0 c)y=0 d) none of these

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

Find the equation for the ellipse that satisfies the given conditions: Major axis on the x-axis and passes through the points (4, 3) and (6, 2).

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

if 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

a tangent to the ellipse x² + 4y²=4 meets the ellipse x²+2y²=6 at P and Q.the angle between the tangents at P and Q of the ellipse x² +2y²=6

35. If P is a point on the hyperbola 16 x² - 9y² =144 whose foci are s₁ and s₂ , then Find PS₁ - PS₂

Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4x + y = 16.

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

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

 how can we derive standard equation of ellipse

The equations of the tangents drawn from the origin to the circle x² + y² - 2rx- 2hy + h²=0 are  :

1. x=0, y=0
2. (h²-r²)x-2rhy=0, x=0
3. y=0,x=4
4. (h²-r²)x + 2rhy=0,x=0.

Find the equation of parabola :

vertex =(2,1)

directrix : x = y-1

Find the coordinate of the point of intersection of the axis and the directrix of the parabola whose focus is (3,3) and the directrix is 3x-4y=2 . find also the latus rectum.

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.

the angle subtended by common tangents of two ellipses 4(x-4)² +25y²=100 4(x+1)² + y²=4 at the origin (in degrees) is

Q Find the equation of the hyperbola with centre as the origin, transverse axis along x - axis, ecentricity √5 and the sum of whose semi - axes is 9.

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 x²+y²-4x-8y-41=0 and is concentric with x²+y²-2y+1=0

prove tht points (2,-4)(3,-1)(3,-3)(0, 0)are concyclic

answer fast.urgent

Find the vertex, axis, focus, directrix, tangent at the vertex, and length of the latus rectum of the parabola:

2y² + 3y - 4x - 3 = 0

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

Find the distance between the chords of contact of the tangent to the circle x² +y² +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.

Show that the circle x^2+y^2-2ax-2ay+a^2=0 touches both the coordinate axes.

If P is any point on hyperbola whose axis are equal,prove that SP.S'P=CP² ?

the straight line kx+y=4 touches the parabola y=x-x^2, if k=?

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