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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.
The length of the chord of the circle x2+y2+4x -7y+12 =0 along the y- axis is
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 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 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?
if an ellipse with major and minor axes of length 10sqrt3 and 3 units respectively slides along the coordinate axes in the first quadrant, then find length of the arc which is formed by the locus of centre of the ellipse.
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 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
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 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.
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?
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
Find the equation of a parabola whose vertex is (1,3) and focus is(-1,1)
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
A circle c1 of radius 1cm touches the x-axis as well as the y-axis, another circle c2 of radius greater than 1cm touches the coordinate axes as well as the circle c1. What is the radius of the circle c2?
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
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 ?
Let L1 be a straight line through the origin and L2 be a straight line x + y = 1. If the intercepts made by the circle x2 + y2 -x + 3y =0 on L1 and L2 are equal , then find the equation(s) which represents L1 .
what is angle between asymptotes of hyperbola
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 angle between the tangents drawn from the point (-a,2a) to y^2=4ax is :
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
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 concept of chord of contact of a circle for itt jee questions.
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?
If two circles touching both the axes are passing through (2,3) then lengths of their common chord is
Equation of an ellipse is x2+ y2+ xy + 1 = 0.
(1) Length of largest chord = ?
(2) Length of chord perpendicular to the chord asked in (1) , passing through the center of ellipse = ?
The equation of the asymptotes of the hyperbola 2x2+5xy+2y2-11x-7y-4=0 are. Urgent plz post asap
A tangent is drawn at any point P(t) on parabola y2=8x where P(t) :x-coordinate = 2t2, y-coordinate = 4t . On this tangent, a point Q(a,b) is taken, from which pair of tangents QA and QB are drawn to circle x2+ y2= 4.
(1) Find equation of locus of point of concurrency of chord of contact AB of the circle.
(2) Find equation of locus of circumcentre of triangle AQB if t = 2.
perpendiculars are drawn from two points on the axis of the parbola y^2=4ax to a tangent to the parabola. if the points are situated at a distance d from the focus and the lengths of the perpendicualrs are p1 and p2 . then p1^2-p2^2:
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse
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 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 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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