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find the locus of the mid point of a chord of a circle x2 +y2=4 which subtends a right angle at the origin?
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
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.
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 ?
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 vertex latus rectum, focus, axis , equation of directrix in standard form and transform them with respect to original axes.
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
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
The least distance of the chord passing through (2 , 1) of the circle x^2+y^2-2x-4y-13=0
A) 2 B) 6 C) 8 D) 4
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?
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 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.
the locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix
(a) x = -a
(c) x = 0
The least distance of the line 8x-4y+73=0 from the circle 16x^2+16y^2+48x-8y-43=0 is
A) (square root of 5)/2 B) 2*square root of 5 C) 3*square root of 5 D) 4*square root of 5
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 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 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
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
A circle touches the y axis at 0,3 and cuts and interept of 8 units on x axis pls explain me the doubts
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
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
The midpoint of the chord 4x-3y=5 of the hyperbola 2x^2-3y^2=12 is
A) (0 , -5/3) B) (2 , 1) C) (5/4 , 0) D) (11/4 , 2)
The radius of circle having maximum size passing through (2,4) and touching both the coordinate axes is- Answer is 10 please explain
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 line xcosA +ysinA =p intersects the circle x2+y2=4 at A and B . If the chord AB makes an angle 30o at a point on the circumference of the circle , then A) p2=3 B)p2=4cos215degrees C) p2=2 D)p2=6
the angle between the tangents drawn from the point (-a,2a) to y^2=4ax is :
If the chords of the hyperbola x2-y2=16 touches the parabola y2=16x, then the locus of the middle points of these chords is the curve
A) y2(x+4)=x3 B) y2(x-4)=x3 C) y2(x-2)=3x3 D) y2(x-8)=2x3
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
find the euation of parabola whose focus is (1,-1) and whose vertex i (2,1) .Also find the latus rectum
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 right angled isosceles triangle is incribed in the circle x2+y2-4x-2y-4=0 then length of its side is
A) square root of 2 B) 2*square root of 2 C) 3*square root of 2 D) 4*square root of 2
If two circles touching both the axes are passing through (2,3) then lengths of their common chord is
The equation of the asymptotes of the hyperbola 2x2+5xy+2y2-11x-7y-4=0 are. Urgent plz post asap
Two circles , each of radius 5, have a common tangent at (1,1) whose equation is 3x + 4y - 7 = 0. Then their centres are
a. (4,-5), (-2,3)
b. (4,-3), (-2,5)
c. (4,5), (-2,-3)
A) 2 B) -1 C) -2 D) 3
tangents are drawn from the parabola y^2=4ax to the parabola y^2=4b(x-c) find the locus of the mid-point of the chord of contact
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 :
The equation of the circle whose diameter lies on 2x + 3y = 3 and 16x - y = 4 and which passes through (4, 6) is
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