Recently Active Co Ordinate Geometry Questions

1. If the vectors a=3i+j-2k, b=-i+3j+4k and c=4i-2j-6k constitute the sides of triangle ABC, then find the length of the median bisecting the the vector c. ...

If the vectors 3p+q;5p-3q and 2p+q;4p-2q are the pairs of mutually perpendicular vectors then find the value of sin(p^q). ...

Find the set of values of c for which the angle between the vectors cxi-6j+3k and xi-2j+2cxk is acute for every xξR ...

I know vectors....but I find these triangle questions difficult.....plz help me in these... In triangle ABC , O,N,G,O' are circumcentre ,nine point centre ,centroid,orthocentre respectively.AL and BM are perpendiculars from A ...

In ΔABC if points D,E,F are taken on sides BC,CA,AB respectivaly so that BD/DC=CE/EA=AF/FB=n/1....and areaΔDEF/areaΔABC=λ/[2(n2-n+1)/(n+1)2] find λ ...

sides BC,CA ,AB of ΔABC are divided by points P,Q,R in ratios BP/PC=λ,AR/RB=ν,CQ/QA=μ, than calculate area ΔPQR/area ΔABC ...

if a,b,c are non coplanar unit vectors such that a X(bXc)=b+c/ 2 then the angle between a and b is: ...

what is the max no of rational pts on a circle's circumference which is centred at (Ï€,e) ...

The chord AC of the parabola y2=4x subtends 900 angle at points B and D on the parabola . If A , B, C, D are represented by t1 , t2 , t3 , t4 then , show and find the relation BETWEEN t1 , t2 , t3 , t4 . ...

Same problem as priyam......couldnt resist using latex 3 tangents are drawn to hyperbola xy=c^{2} at the points (x_{i},y_{i}):i=1,2,3.... and form a triangle whose circumcircle passes through centre of hyperbola.Show that \fr ...

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Q1. If a quadrilateral formed by four tangents to the ellipse 4x2+5y2=20 is a square then: (a) the vertices of the square lie on y=±x (b) the vertices of the square lie on x2+y2=9 (c) the area of all such squares is a consta ...

Show that the locus of the point that divides a chord of slope 2 in the ratio 1:2 is a parabola. Find the vertex of the parabola obtained! ...

Find the equation of the chords of the parabola y2=4ax which passes through the point (-6a,0) and which subtends an angle of 45° at the vertex. ...

Find the equation of the circle that passes through the focus of the parabola x2=4y and touches the parabola given at the point (6,9). (My specific doubt is that we can form the two equations from the two given points but whe ...

Through the vertex O of the parabola y2=4ax, chords P and Q are drawn at right angles to one another. Show that for all positions of point P, PQ cuts the axis of the parabola at a fixed point. Also find the locus of middle po ...

9) Number of points outside the hyperbola (x2/25) - (y2/36) =1 , from where two perpendicular tangents can be drawn to the hyperbola is(are) a> 3 b> 2 c > 1 d>0 16) If a circle x2+y2=4 intersects a rectangular hyp ...

|a|=2,a.b =1,angle between a and b = 60 . r is any vector satisfying: r.a=2 r.b=8 (r+2a-10b).(a x b) = 4 3 (r+2a-10b) = λ(a x b) then λ = A)1/2 B)2 C)1/4 D)4 ...

The set of points on the asix of the parabola 2((x-1)2+(y-1)2)=(x+y)2. , from which 3 distinct normals can be drawn to the parabola , is the set of points (h,k) lying on the axis of the parabola such that a) h>3 b) h>3/ ...

If the lines a1x+b1y+c1=0; a2x+b2y+c2=0 cut the coordinate axes in concylic pts , then give the relation between a1,a2,b1,b2 I think this qn shud be done in 2mins but i cant do it ,still i cant get ne desired results. pls pos ...

check these ques out from t 26 Q8) Find the eqn. of the line which is at distance 5 from origin it makes an angle of 120o with +ve x-axis. a) x+√3y-10=0 b) √3x+y-10=0 c) √3x+y-5=0 d) √3x-y-10=0 Q2) The two points of a ...

A circle of variable radius is given by x2+y2+2gx+2fy+c=0 cuts the rectangular hyperbola x2-y2 = 9a2 in points P, Q, R and S at (xiyi) (i = 1,2,3,4) find centroid of triangle PQR ! ...

stat1 : the eqn √x + √y =1 represents a part of the parabola. stat2 : the curve √x + √y =1 lie in the first quadrant only. ...

stat1 : if eccentricities of two ellipses are same then their areas are also same. stat2 : (a2 - b2)/a2 = (a'2 - b'2)/a'2 ...

Match the following Consider the linear equations. ax+by+cz=0 bx+cy+az=0 cx+ay+bz=0 (A) a+b+c≠0 and a2+b2+c2=ab+bc+ca (B) a+b+c=0 and a2+b2+c2≠ab+bc+ca (C) a+b+c≠0 and a2+b2+c2≠ab+bc+ca (D) a+b+c=0 and a2+b2+c2=ab+bc+ ...

no of planes which are at a given perpendicular distance from a given point and passing through a given point is : a) 0 b) 2 c) 4 d) infinity ...

Radius (R<4) of a O which touches the circle x2+y2=16 externally and angle between the direct common tangents is tan-1(24/7) is __ ...

In a triangle ABC, coordinates of A are (1, 2) and the equations to medians through B and C are x + y = 5 and x = 4 respectively. Then, 14. The coordinates of the vertex C are (A) (5, 3) (B) (3, 4) (C) (4, 3) (D) (3, 5) 15. L ...

no of planes that are equidistant from four non-coplanar points is : a) 3 b) 4 c) 7 d) 9. visualised the situation and answered... but someone give me a 'nice' method ... in the sence a 'way' to actually 'solve' ... ...

consider a triangle AOB in the x-y plane where A(1,0,0) , B(0,2,0) , O(0,0,0). the new position of O , when triangl is rotated about side AB by 90° can be ... a) 4/5,3/5,2/√5 b)-3/5,√2/5,2/√5 c) 4/5,2/5,2/ 5 d) 4/5,2/5 ...