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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?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.

^{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 ??Find the equation of the circle passing through (0, 0) and making intercepts

aandbon the coordinate axes.^{2}=4ax is of length 8a. prove that the lines joining the vertex to its two ends are at right angles.^{2}/9 +y^{2}/5=1 (iit asked question)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 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.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 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.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 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}= 9axFind the equation of a parabola whose vertex is (1,3) and focus is(-1,1)

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 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

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?

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.

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 briefly^{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 circleA 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 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 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

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

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

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

^{2}/a^{2}^{}+ y^{2}/b^{2}=1 is x^{2}/a^{2 }+ y^{2}/b^{2}=ex/a_{1},y_{1}) and (x_{2},y_{2}) lying on the parabola y^{2}=4ax is (y-y_{1})(y-y_{2})=y^{2}-4ax.^{2}+y^{2}+4x-4y+4=0, which makes equal intercept on the positive coordinate axes is:^{1/2}If two circles touching both the axes are passing through (2,3) then lengths of their common chord is

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

what is angle between asymptotes of hyperbola

^{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}????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}+y^{2}-6x+2y-28=0^{2}- 2x + 3 .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

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.

^{2}/a^{2}+ y^{2}/b^{2 }= 1 with R and S as the two focii. Find the maximum area of the triangle PRS^{2}/9 - y^{2}/4 =1 ,parallel to the straight line 2x -y =1 .The points of contact of the tangent on hyperbola are....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+2Pls 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}/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}α^{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})^{2}+y^{2}=8 makes equal intercepts of length 'a' on the co-ordinate axes ,then:^{1/2}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.

A] lies inside of the circle

B] lies outside of the circle

C] lies on the circle

D] does not exist.

REPLY SOON PLSS

The equation of the asymptotes of the hyperbola 2x

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

B] form an equilateral

C] form a right angled triangle

D] passes through the centre of the circle

^{2}=8x as a diameter. show that this circle pases through the point of intersection of the axis and the directric of the parabola.^{2}=4ax to its directrix and SPMis an equilateral triangle('S' is a focus),then SP=???(a>0)..^{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})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)

a.2sin18

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

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

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

If then lines

(y-b) = mand_{1}(x+a)(y-b) = mare the tangets to the parabola y_{2}(x+a)^{2}=4ax, then:A) m

_{1}+m_{2}= 0B) m

_{1}m_{2}= 1C) m

_{1}m_{2}= -1D) m

_{1}+m_{2}= 12x+3y=2

3x-2y=4

x+2y=3

2x-y=3