If the orthocenter of a triangle whose vertices are (1,2),(2,3),(3,1)

 

P. If the orthocenter of a triangle whose vertices are (1,2),(2,3),(3,1) is (alpha, beta). Then the quadratic equation whose roots are alpha+4beeta and 4alpha+beta is

(JEE Main2023(online)1st February morning shift)

(Our YouTube channel: Maths Solutions by HPL)

Solutions to the below questions are also available in our You tube channel

1. The equation of the sides AB,BC and CA of a triangle ABC

2. Let m1 and m2 be the slopes of two adjacent sides

3. Let A(1,1),B(-4,3),C(-2,-5) be vertices of a triangle ABC

4.  Let A be the set of all points (α, β) such that the

5. In an isosceles triangle ABC, the vertex A is (6,1) and

6. Let A(α,-2),B(α,6),C(α/4,-2) be vertices of ∆ABC. If

7. Let the circumcenter of a triangle with vertices A(a,3)

8. If the perpendicular bisector of the line segment joining the points

9. The set of all possible values of θ in the interval (0,π) for which the points

10. Let B and C be the 2 points on the line y+x=0 such that

11. If the orthocenter of a triangle whose vertices are (1,2),(2,3),(3,1)

12. Let the point P (α,β) be at a unit distance from each

13. A line with the slope greater than one passes through

14. A point P moves so that the sum of squares of its distance

15. Let a triangle be bounded by the lines L1:2x+5y=10;L2

16. let-alpha1,alpha2,are two values of alpha for which t

17. Distance of the origin from the centroid of the triangl

18. The distance between the two points A and A ' which lie

19. If two straight lines whose direction cosines are given

20. Let R be the point (3,7) and let P and Q be two points

21. Let the area of the triangle with vertices A(1, α), B(α,

22. If p and q are the lengths of the perpendiculars from

23. Let A be a fixed point (0,6) and B be a moving point

24. The angle between the straight lines whose direction

25. The point P(a,b) undergoes the following three transformation

26. Two sides of a parallelogram are along the lines 4x+5y=

27. Let the centroid of an equilateral triangle ABC

28. Let the equation of the pair of lines y = px and y=qx

29. The number of integral values of m so that the

30. The equation of one of the straight lines which passes through the point

31. In a triangle PQR, the coordinates of the points

32. Let A(-1,1),B(3,4) and C(2,0) be given three

33. The intersection of 3 lines x-y=0,x+2y=3&

34. The image of the point (3,5) in the line

35. Let L denote the line in the xy-plane with x and y intercepts as 3 and 1

36. A ray of light coming from the point (2,2√3) is

37. Two vertical poles AB=15m and CD=10m are standing apart on a horizontal ground

38. If a triangle ABC has vertices A(-1,7),B(-7,1)