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Syllabus

find the locus of the mid point of a chord of a circle x

^{2}+y^{2}=4 which subtends a right angle at the origin?The length of a focal chord of the parabola y

^{2}= 4ax at a distance b from the vertex is c , thena. b

^{2}c = 4a^{3}b. bc

^{2}= 4a^{3}c. 4bc = a

^{2}d. a

^{2}b = 4c^{3}Explain briefly.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

aandbon the coordinate axes.^{2}/9 +y^{2}/5=1 (iit asked question)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

A parabola having equation 4y

^{2}+12x-20y+67=0 has its origin shifted to a point (h,k) such that the equation becomes the standard equation y^{2}=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 length of focal chord of the parabola y

^{2}= 4ax making an angle~~o~~with the axis of the parabola isa. 4a cosec

^{2}~~o~~b. 4a sec

^{2}oa cosec

^{2}~~o~~d. n.o.t.

Explain briefly.^{2}/2g sin2α , -u^{2}/2g cos2α) and the directrix is y= u^{2}/2g isu

^{2}/g cosαu

^{2}/g cos^{2}2^{}α2u

^{2}/g cos2^{}α2u

^{2}/g cos^{2}αThe locus of the point of trisection of the double ordinates of the parabola

y

^{2}= 4ax isa) y

^{2}= 4ax b) 9y^{2}= 4ax c)9y^{2}= ax d) y^{2}= 9axThe 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 = c

^{2}at the point 't_{1}' meets the curve again at the point 't_{2}'. The value of t_{1}^{3}.t_{2}isa. 1

b. c

c. -c

d. -1

A square is inscribed in the circle x

^{2}+y^{2}-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 y

^{2}= 4ax is another parabola with directrix(a) x = -a

(b)

(c) x = 0

(d)

^{2}=4ax is of length 8a. prove that the lines joining the vertex to its two ends are at right angles.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(ap

^{2},2ap) meets the parabola y^{2}= 4ax again at Q(aq^{2},2aq) such that the lines joining the origin to P and Q are at right angle . Thena. p

^{2}=2b. q

^{2}=2c. p =2q

d. q =2p

Please explain brieflyThe 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.

x

^{2}+y^{2}=a^{2}x

^{2}/a^{2}+ y^{2}/b^{2 }=2x

^{2}+y^{2}=b^{2}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

^{2}+y^{2}+4x+6y+13=0 represents a) a pair of coincident lines b) a pair of concurrent lines c) a parabola d)a point circle^{2}+y^{2}+4x-4y+4=0, which makes equal intercept on the positive coordinate axes is:^{1/2}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

^{2}+y^{2}-4x-8y-5=0 in two points then the limits of k areThe 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)x

^{2}+y^{2}-6x-6y+9=0b)4(x

^{2}+y^{2}-x-y)+1=0c)4(x

^{2}+y^{2}+x+y)+1d)none of these

^{2}=8x is y=x+2. prove that The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is (-2,0).^{2}- 2x + 3 .^{2}/a^{2}^{}+ y^{2}/b^{2}=1 is x^{2}/a^{2 }+ y^{2}/b^{2}=ex/aThe 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

^{2}/9 - y^{2}/4 =1 ,parallel to the straight line 2x -y =1 .The points of contact of the tangent on hyperbola are....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?

^{2}/a^{2}+ y^{2}/b^{2}=1 then prove that a^{2}/l^{2}+b^{2}^{}/m^{2}= (a^{2}-b^{2})^{2}/n^{2}????^{2}+y^{2}-6x+2y-28=0The line xcosA +ysinA =p intersects the circle x

^{2}+y^{2}=4 at A and B . If the chord AB makes an angle 30^{o}at a point on the circumference of the circle , then A) p^{2}=3 B)p^{2}=4cos215degrees C) p^{2}=2 D)p^{2}=6the 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

^{2 }+ 4y^{2}= 4 in points, whose eccentric angles differ bypie/3 , then prove that r

^{2}= 3/4 (4p^{2} +q^{2})? ? please explain what eccentric angle refer to ??^{2}/a^{2}+ y^{2}/b^{2 }= 1 with R and S as the two focii. Find the maximum area of the triangle PRSIf the chords of the hyperbola x

^{2}-y^{2}=16 touches the parabola y^{2}=16x, then the locus of the middle points of these chords is the curveA) y

^{2}(x+4)=x^{3 }B) y^{2}(x-4)=x^{3 }C) y^{2}(x-2)=3x^{3 }D) y^{2}(x-8)=2x^{3}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

^{2}=8x and xy=-1 is y=x+2find 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?

^{2}/a^{2 }+ y^{2 }/b^{2 }=1 and a concentric circle of radius r is ( r^{2}-b^{2})^{1/2}/(a^{2}-r^{2})Find the equation of a parabola whose vertex is (1,3) and focus is(-1,1)

2x+3y=2

3x-2y=4

x+2y=3

2x-y=3

The length of the chord of the circle x

^{2}+y^{2}+4x -7y+12 =0 along the y- axis isa. 1

b. 2

c. 1/2

d. n.o.t.

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 2x

^{2}+5xy+2y^{2}-11x-7y-4=0 are. Urgent plz post asapTwo 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)

d. n.o.t.

^{2}=4ax to its directrix and SPMis an equilateral triangle('S' is a focus),then SP=???(a>0)..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

h

^{2}/a^{2}+k^{2}/b^{2}=1h

^{2}/a^{2}+k^{2}/b^{2}=2a

^{2}/h^{2}+b^{2}/k^{2}=1none of the above

a.2sin18

^{o}b.2cos18^{o}c.2sin54^{o}d.2cos54^{o}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

^{2},a-2) be a point interior to the region of the parabola y^{2}=2x bounded by the chord joining the points (2,2)and (8,-4)then the set of all possible real values of a, is---(A) (-2,2^{1/2}) (B) (-3,2) (c)(-2,2^{1/2}) (D) (-2,-2+2^{1/2})what does it mean by parametric equation of parabola?

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

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