Newest Co Ordinate Geometry Questions

the equation e^(x-1)+x-2=0 has how many roots ?????????? ...

Find the sum of the the intercepts on the axes of coordinates by any tangent to the curve √x +√y=2 Plz solve this problem............ ...

Let P be an interior point of a triangle ABC. Extend AP, BP, CP to meet BC, CA, AB respectively in D, E, F. Suppose the areas of the triangles APE, APF and BPD are equal, prove that P is the centroid of triangle ABC. ...

For a > 0, prove that the circle x2 + y2 =1 and the parabola y=ax2 - b intersect at four distinct points, provided a>b>1. This is the solution given in my book. Since a>0, by figure -b<-1 i.e. b>1 also when ...

Coming back after a long time..... The question: Prove that a point can be found which is equidistant from each of the following four points: A (a m1, a/m1), B (a m2, a/m2), C (a m3, a/m3), and D (a/m1m2m3, a m1m2m3) ...

Find the equation of the circle described on a focal chord with slope m, of the parabola y2=4ax as diameter. There are two approaches to this problem. 1) The end points of the focal chord are (a/m2,2a/m) and (am2,-2am) So the ...

If m is the slope of a line and 3m+4=3m+2 then does this line exist or not?? ...

1.THE POINTS (a,b), (c,d),(a,d),(c,b) TAKEN IN ORDER, WHER a,b,c,d are real numbers are: a. COLLINEAR b. VERTICES OF A SQUARE c. VERTICES OF A RHOMBUS d. CONCYCLIC given ans:: b but my answer:: d PLEASE EXPLAIN IN DETAILS ...

If the pair of lines x^2 - 2pxy - y^2=0 and x^2 - 2qxy - y^2=0 are such that each pair bisects the angle between the other pair, then pq equals.? The solution is The second pair must be identical with x^2 - y^2/1-(-1) =xy/-p ...

Plz help 1.find the area of traingle formed by the lines y-x=0;x+y=0 and x-k=0. 2.the line 7x-9y-19=0 is perpendicular to the line through the points(x,3) and (4,1), find the value of x. ...

If the locus of the mid points of the chords of the circle x2+y2=16 which are tangents to the hyperbola 9x2-16y2=144 is given by (x2+y2)a= bx2-cy2 then find the value of a+b+c. ...

1.Tangents at the three points of a parabola y^2 = 4ax form a equilateral triangle . Prove that the vertices of the triangle lie on the curve (3x + a)(3a + x) = y^2 2.Prove that the normal to the parabola y^2 = 4ax at (am^2, ...

not a doubt... Prove that the straight lines joining the origin to the points of intersection of the straight lines hx+ky=2hk and the curve (x-k)2+(y-h)2=c2 are at right angles if h2+k2=c2 ...

If A ≡(3,4) and B is a variable point on the line |x|=6.If AB≤ 4 then the no. of positions of B with integral co-ordinates is: a)5 b)10 c)12 d)6 ...

Consider a parabola y=\frac{x^{2}}{4} and the point F (0, 1). Let A1(x1, y1), A2(x2, y2), A3(x3, y3),........, An(xn, yn) are 'n' points on the parabola such xk > 0 and <OFA_{k}=\frac{k\Pi }{2n} (k=1,2,3,....,n) . Then ...

If G is the centroid and I the in-centre of the triangle, with vertices A(-36,7), B(20,7) and C(0,-8), then, find the value of GI. ...

1. In a tri ABC the median AD and the altitude AM divides the angle A in three equal parts.Show that \Delta (cos A/3.sin2A/3) = 3a3 /128R . 2. In a \Delta abc the lengths of the bisectors of the angles A, B and c are x,y and ...

re^{-r/2}cos\theta =constant where r is the radial distance of the point from origin and theta is the colatitude (angle btw the radial vector and the one pointing towards the z coordinate of the point)) ...

A point moves such that the sum of the squares of its distances from two intersecting straight lines is constant. a)identify which conic it is b)find the eccentricity of the conic in terms of the angle between the straight li ...

show thet the length of the radius vector of the ellipse x2/a2 + y2/b2 =1 drawn in the direction making an angle θ with the positive directtion of x-axis is √( a2b2/b2cos2θ+a2sinθ ) Also show that the sum of the reciproc ...

In triangle ABC the coordinates of the vertex A are (4,-1) and the lines x-y-1=0 and 2x -y = 3 are internal bisectors of angles B and C then , radius of incircle of triangle ABC is ...

Find the length of the chord of the ellipse x2/25 + y2/16 = 1 , whose middle point is ( 1/2 , 2/5 ) . ...

1. Two rods of lengths a and b side along coordinate axis in a manner that their ends are always concyclic. Find the locus of the centre of the circle passing throw these ends. 2.The base of a triangle passes throw a fixed po ...

*Image* *Image* Prove it from both Sides : 1. Co ordinate Geometry 2 . Euclidean Geometry (Normal Geometry) Separately ...

Find the values of x; y for which x2 + y2 takes the minimum valuewhere (x + 5)2 + (y-12)2 = 142. ...

The question in which I am having a problem is as follows: Prove that the point on the curve y2=x,at which a tangent makes an angle of 450 with the x-axis is ( 1/4 , 1/2 ) My doubt: If we find the equation of a tangent at the ...

Find out the coordinates of the extremities of the latus rectum of the parabola x2+y2-16x-16y+2xy+32=0. ...

1.The equation of the parabola whose vertex is origin, axis is along y-axis and which passes through the point (2,1) is 2.The vertex and focus of a parabola are at a distance are at a distance of h and k units on positive x-a ...

1)Find the equation to the straight line which passes through the given point (x',y') and is such that the given point bisects the part intercepted between the axes. 2) Find the eauation to the straight line which passes thro ...

What is the Diff between eccentric angle and parametric points of an ELLIPSE? DO NOT TELL THE DEFINITION but tell me if they can be used interchangeably as I have seen in some ques............. ...