Straight Lines questions
982 published questions with worked solutions.
- If the real part of z+2 z-1 is 4, then the locus of the point representing z in the complex plane is
- Let z_1,z_2,z_3 be the affixes of the vertices of a triangle having the circumcentre at the origin. If z is the affix of it's...
- The locus of the centre of the circle which touches the circles |z-z_1|=a and |z-z_2|=b externally (z, z_1 and z_2 are complex...
- If Im ( 2z+1 iz+1 )=-2, then locus of z is
- The locus of point z satisfying Re (z^2 )=0, is
- Let 3-i and 2+i be affixes of two points A and B the argand plane and P represents the complex number z=x+iy. Then, the locus of...
- The complex equation of straight line L is (4+3i)z+(4-3i) z=24. Find the area of the triangle formed by L, real and the imaginary...
- Let the mid points of the sides of a triangle ABC be ( 52, 7 ), ( 52, 3 ) and (4, 5). If its incentre is (h, k), then 3h + k is...
- Let the vertex A of a triangle ABC be (1, 2), and the mid-point of the side AB be (5, −1). If the centroid of this triangle is...
- Let P(3cosα, 2sinα), α≠0, be a point on the ellipse x²/9+y²/4=1, Q be a point on the circle x²+y²−14x−14y+82=0 and R be a point...
- From the point (−1,−1), two rays are sent making angles of 45° with the line x+y=0. These rays get reflected from the mirror...
- In an equilateral triangle PQR, let the vertex P be at (3,5) and the side QR be along the line x+y=4. If the orthocentre of the...
- If a straight line drawn through the point of intersection of the lines 4x + 3y − 1 = 0 and 3x + 4y − 1 = 0, meets the...
- A ray of light coming from the point P(1, 2) gets reflected from the point Q on the x-axis and then passes through the point R(4,...
- A variable line L passes through the point (3, 5) and intersects the positive coordinate axes at the points A and B. The minimum...
- Let R be the interior region between the lines 3x – y + 1 and x + 2y – 5 = 0 containing the origin. The set of all values of a,...
- If the sum of squares of all real values of α, for which the lines 2x – y + 3 = 0, 6x + 3y + 1 = 0 and αx + 2y – 2 = 0 do not...
- If (a, b) be the orthocentre of the triangle whose vertices are (1, 2), (2, 3) and (3, 1), and I_1 = _a^b x (4x - x^2)dx, I_2 =...
- The portion of the line 4x + 5y = 20 in the first quadrant is trisected by the lines L₁ and L₂ passing through the origin. The...
- Let for any three distinct consecutive terms a, b, c of an A.P., the lines ax + by + c = 0 be concurrent at the point P and Q(α,...
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