find the locus of the mid point of a chord of a circle x² +y²=4 which subtends a right angle at the origin?

Find the equation of a circle which touches y-axis at a distance of 4 units from the origin and cuts an intercept of 6 units along the positive direction of x- axis.

Find the equation of the circle passing through (0, 0) and making intercepts a and b on the coordinate axes.

The length of a focal chord of the parabola y² = 4ax at a distance b from the vertex is c , then

a. b²c = 4a³

b. bc² = 4a³

c. 4bc = a²

d. a²b = 4c³

Explain briefly.

The length of focal chord of the parabola y² = 4ax making an angle o with the axis of the parabola is

a. 4a cosec²o

b. 4a sec²o

a cosec²o

d. n.o.t.

Explain briefly.

The locus of the point of trisection of the double ordinates of the parabola

y² = 4ax is

a) y² = 4ax b) 9y² = 4ax c)9y² = ax d) y² = 9ax

a tangent to the parabola y2=8x makes an angle of 45 degree with the straight line y=3x+5.then what is the equation of tangent?

A square is inscribed in the circle x²+y²-2x+4y+3=0.its side are parallel to the coordinate axes.find the one vertex of the square.

let 2x^(2)+y^(2)-3xy=0 be the equation of a pair of tangents drawn from the origin O to a circle of radius 3 with center in the first quadrant. if A is one of the points of contact find length of OA?

The normal at the point P(ap²,2ap) meets the parabola y² = 4ax again at Q(aq²,2aq) such that the lines joining the origin to P and Q are at right angle . Then

a. p² =2

b. q² =2

c. p =2q

d. q =2p

Please explain briefly

A parabola having equation 4y²+12x-20y+67=0 has its origin shifted to a point (h,k) such that the equation becomes the standard equation y²=4aX.

Find h,k

Find vertex latus rectum, focus, axis , equation of directrix in standard form and transform them with respect to original axes.

The equation of a circle touching x=0,y=0,x=4 is

a man has 7 relatives, 4 of them are ladies and 3 gentlemen, his wife has 7 realtives and 3 of them are ladies and 4 gentlemen. in how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man's relatives and 3 of wife's relatives?

i want this answer in steps.

If the chord y=mx+1 of the circle x^2+y^2=1 subtends an angle of measure 45 degrees at the major segment of the circle then m is

A) 2 B) -1 C) -2 D) 3

The normal to the rectangular hyperbola xy = c² at the point 't₁' meets the curve again at the point 't₂'. The value of t₁³.t₂ is

a. 1

b. c

c. -c

d. -1

A circle touches the y axis at 0,3 and cuts and interept of 8 units on x axis pls explain me the doubts

1. What is the differrence between touhing and forming intrcept?
2. The radius =8 so can we solve the eqn of circle by the points 0,3 and 8,0
3. pls explain me the easiest method with formula

thanks in advance

The line x+y=1 cuts the coordinate axes at P and Q and a line perpendicular to it meet the axes in R and S. The equation to the locus of the point of intersection of the lines PS and QR is

A) x2+y2=1 B) x2+y2-2x-2y=0 C) x2+y2-x-y=0 D) x2+y2+x+y=0

The equation of the incircle of the triangle formed by the axes and the line 4x+3y=6 is

a)x²+y²-6x-6y+9=0

b)4(x²+y²-x-y)+1=0

c)4(x²+y²+x+y)+1

d)none of these

The equation of the image of the circle x^2+y^2-6x-4y+12=0 by the line mirror x+y-1=0 is

A) x^2+y^2+2x+4y+4=0 B) x^2+y^2+x+y=0 C) x^2+y^2-2x-4y+4=0 D) x^2+y^2-2x-4y-4=0

1. x+y=2
2. x+y=2(2)^1/2
3. x+y=4
4. x+y=8

If f1 and f2 be the feet of the perpendicular from foci s1 and s2 of an ellipse (x²/5) + (y²/3) =1 on the tangent at any point P on the ellipse, then (s1f1)(s2f2) is equal to ?

Ans --3

what is angle between asymptotes of hyperbola

The point of intersection of the tangent at 2 points on the ellipse whose ecentricity differs by 90 degree , how can we write this stmt?

the angle between the tangents drawn from the point (-a,2a) to y^2=4ax is :

1) pi/4

b)pi/2

c)pi/3

d)pi/6

a- the common tangent to the circle x2+y2=6xand x2+y2+2x=0 forms an........... triangle

b-if 2 distinct chords of circle x2+y2=ax+by r drawn from pt a,b are divided by the x axis in 2;1 find relation b/w a and b

c- find eqn of locus of feet of perpendicular drawn from origin upon a variable chord of a circle which subtend right angle at origin

Pls explain the question LET C BE A CIRCLE ITH CENTRE 0,0 AND RADIUS = 3 UNIT THEN THE EQUATION OF THE LOCUS OF THE MID POINTS OF THE CHORD THAT SUBTEND AN ANGLE = 2PI/3?

Find the equation of a parabola whose vertex is (1,3) and focus is(-1,1)

The length of the chord of the circle x²+y²+4x -7y+12 =0 along the y- axis is

a. 1

b. 2

c. 1/2

d. n.o.t.

If two circles touching both the axes are passing through (2,3) then lengths of their common chord is

The pole of a straight line with respect to the circle x2+y2=a2 lies on the circle x2+y2=9a2 If the straight line touches the circle x2+y2=r2 then a)9a2=r2 b)9r2=a2 c)r2=a2 d)3r2=a2 Answer is (2) op[tion Plss explain it.

The equation of the asymptotes of the hyperbola 2x²+5xy+2y²-11x-7y-4=0 are. Urgent plz post asap

The equation of the circle whose diameter lies on 2x + 3y = 3 and 16x - y = 4 and which passes through (4, 6) is

AB is a chord of the parabola y^2=4ax wih its vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the axis of the parabola is :

a) a

b) 2a

c) 4a

d)8a